Hi! My answer isn’t perfect but i hope it clears some things up for you:
B) C) and D) would explain a change in genotype not karyotype
E) is wrong as homologous recombination happens with 2n=4 chromatids, (and the image does in fact show a chromosome undergoing homologous recombination with 2n=4). All the chromatids are accounted for.
A) we are left with this option by elimination, i’m not sure why it’s correct.
Translocation is a type of karotype modification so it could be a possible answer.
Does someone have a better explanation? Let me know if i’m wrong 
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