How can evolution cause 2 pairs of chromosomes to fuse while still generating viable offspring?

Chromosomal changes are surprisingly (at least it surprises me) common between closely related species. Having an odd number of chromosomes doesn't absolutely preclude fertility.  Mules and hinnies, which have 63 chromosomes (vs. the 62 and 64 of their parental species) are notoriously almost always sterile, but there are quite a few recorded instances of mule/horse or mule/donkey fertility.  That said, the more likely scenario is that described by () -- interbreeding between close relatives who share the initial fusion.

Differences in chromosome numbers do not always lead to infertility. In fact there are a few common centric fusions, also known as Robertsonian translocations, that occur in humans and they do not affect fertility. During meiosis, the non-fused chromosomes will pair with the right parts of the fused chromosomes because the DNA sequence is basically the same, so sperm and egg cells will be normal in terms of what DNA complement they carry. This has been seen also in domestic sheep, cattle, mouse, and also in Przewalski horse (n=66) and domestic horse (n=64) offspring, these hybrids are fertile.

Biology 101 simplifies and overemphasizes the importance of chromosome number in generating fertile offspring.  Take the next class in cytogenetics, and you'll realize what's more important isn't the number per se, but homology pairing.  That is largely preserved in the case of a individual that is 2n-1 or 2n-2 with fused chromosomes, so meiosis still proceeds normally.http://sapientfridge.org/chromosome_count/fertility.html While it's rarer in animals than plants, some species actually form karyotype series.  Ploidy series are not that rare; sugarcane is notorious for having a large range (2n=48 to 2n=128), as are strawberries (2n=2x=14 to 2n=10x=70).  Here's one example in animals (a butterfly):http://bmcevolbiol.biomedcentral.com/articles/10.1186/1471-2148-11-109 We present the discovery of exceptional intraspecific variability in the karyotype of the widespread Eurasian butterfly Leptidea sinapis. We show that within this species the diploid chromosome number gradually decreases from 2n = 106 in Spain to 2n = 56 in eastern Kazakhstan, resulting in a 6000 km-wide cline that originated recently (8,500 to 31,000 years ago).

Sterility from mismatched chromosomes is a relative thing, not an absolute.There are several known cases of human beings with abnormal chromosome counts from fusion mutations who nevertheless successfully had children. There are reports of mules, supposedly sterile, successfully giving birth to colts.During meiosis, the chromosomes line up with their opposite number and shuffle genes in a process called recombination. After that they are separated in an orderly fashion such that one version of the chromosome goes to one end of the cell and the other goes to the other. The cell then divides, producing two haploid gametes, each with one chromosome from each set. The separation is mediated by a special region in the centre of the chromosome called a centromere.Mutations that change chromosome number only impact fertility if they interfere with this process of lining up and separating, and not all types of chromosome fusion mutations do this.It so happens that the chromosome fusion that occurred in human ancestors is one of the ones that doesn't.In this case, what are now chromosomes 12 and 13 in other apes fused to become chromosome 2 in humans end to end, joining at their telomeres. For simplicity, we'll call the two separate chromosomes A and B, and the fused chromosome AB.Because A and B joined end to end, all the genetic sequences A uses to recognize the other A and line up with it were preserved, and the same with B. The centromeres of both A and B were also preserved.So when the mutation first occurred, the individual in which it happened ends up with one AB, one A and one B. When it came time for this individual to make gametes, A could still line up properly with the A part of AB, and B with the B part of AB, and all three chromosomes could still separate properly because the centromeres were all preserved. Half of the gametes got an AB, and the other half got A and B. All the gametes got the right number of genes so all the gametes are equally viable. There is no penalty to fertility here.So half of this individual's children now have one AB and one A and one B, just like their parent. They, like their parent, have no penalty to fertility. As the generations go on, more and more individuals in the population have an AB. None of these individuals suffer any penalty to fertility.Eventually there are enough individuals with one AB that some of them mate and have children. One quarter of these children have two ABs.Now we have a population in which some people have two ABs, some have one AB, and some still have the separate A and B. All are equally interfertile.Some time later, a small group of this population gets separated from the larger group, preventing exchange of mates and genes.Now at this point a disaster strikes the smaller population. A genetic bottleneck. It could be a disease, or a new predator, or a natural disaster, it doesn't matter. The majority of individuals are killed off. It so happens, by chance, that the only survivors all have double ABs. Because the population is small, the total numbers of people who had separate As and Bs was also small, making it more likely that some random event could kill them all off.The surviving population of double ABs recovers, and continues to be separated from their cousins in the larger population with separate As and Bs. They accumulate new mutations over time, one of which is the loss of one of the two centromeres on their AB chromosome, since they only need one centromere on their fused AB chromosome. Eventually, enough mutations accumulate on their AB chromosomes that even if the barrier that separated them from the separate A and B population is removed, if they try to mate with them, they will produce offspring where the AB chromosome from one parent is sufficiently different from the A and B chromosomes from the other parent that they can't line up and separate properly from one another during meiosis, and these offspring suffer a fertility penalty.Our two populations have now genetically separated. They cannot produce fertile offspring with one another anymore, even if they could meet and mate.They have speciated.