As I understand your question, you appear to have been covered at least from January through May and then again from August through December, so you had a two-month gap.
First, I would ask your parents if you were dropped from their policy immediately upon graduating in May. It's quite possible that they didn't drop you until you had your own insurance in August. It's worth asking, since one of the Affordable Care Act reforms was to allow parents to keep their kids on their policy until age 26.
Being covered on your parents' policy is just as good as having your own policy, when it comes to having qualified medical insurance.
Second, if it turns out that all you have is a two-month gap, then you won't be penalized for not having insurance, because there is an automatic exception for short-term gaps (one or two months).
So find out when you were really dropped from your parents' policy, then complete the table in the Health Coverage section indicating when you did and didn't have insurance.
And if it turns out that you were covered on your parents' policy until August, then just answer that you were insured all year.
NOTE: your parents won’t claim you for half the year - they can't. Either they provided more than half your support in 2016 (in which case, they claim you as a dependent for the year), or you provided more than half your support, so they don’t claim you at all (you claim yourself).
You all will want to review Worksheet 3-1 in Publication 17 to see if you qualify as their dependent or not. Note that the result will also affect how you (or they) report expenses for your college education.
