You can think of ploidy as how many copies of each chromosome are present. The vast majority of human somatic cells have 46 chromosomes total, but these are actually 2 sets of 23. We get one set (of 23) from our mother and one from our father; hence we have 2 copies of each chromosome, so the "ploidy" of humans is 2n, or diploid. Human gametes, containing only 1 set of 23 chromosomes, are haploid, or n. So when egg meets sperm, a simple math problem can represent fertilization: n + n = 2n! Two haploid gametes come together to make a diploid zygote.
According to the question, one round of nuclear replication and two additional rounds of DNA replication have happened. That means that the genome has been copied (or doubled) 3 consecutive times.
1. First round of replication: 2n*2= 4n
2. Second round of replication: 4n*2= 8n
3. Third round of replication: 8n*2= 16n
The answer is 16n (confirmed because I took the same practice exam).
***Important to note: I think this was a poorly written question. The organism in the passage was Giardia, and nowhere in the passage did they specify that the ploidy prior to encystation was 2n. What if the ploidy at that point in the Giardia lifecycle was n? Then the answer would have been 8n. I'm pretty sure the MCAT does not require students to memorize the ploidy of organisms other than humans.