How does crossing over result in a gamete having 3 chromosomes?

Crossing over should not effect a gametes' chromosome number. In crossing over, homologous chromosomes swap information--this does not change the number of chromosomes, it just creates new combinations of information as the two chromosomes swap parts.

Crossing over occurs before the final division that halves the chromosome number and creates a gamete with only "n" chromosomes (as opposed to "2n," which is the number that normal body cells have). The reduction of chromosome number happens in this second meiotic division, not during crossing over.

Hope this helps!