Hypothesize one way that a diploid organism could have offspring that are 3n or 4n

Popypoidy mainly occurs in the plants when there is total non-disjunction of sister chromatids occurs during the meiosis of gametic cells. So as before the meiosis the number of chromosomes doubles and after meiosis every cell get half the number of chromosome so after segregation failure autopolyploidy occurs in plants.

Triploid condition can also be seen in animals when two sperms fertilize one ovum. So, in this case, the chromosome number reaches to 69(23+23+23) which means chromosome number become 3n.