Hey there!
For this problem, analyze each sentence you've been given:
"Assateague is a large island off the coast of Virginia; it is inhabited by wild ponies." When you use a semicolon, you are essentially combining two related whole sentences, not fragments, into one sentence. What would make the most sense is "Assateague is a large island off the coast of Virginia. It is inhabited by wild ponies." So, this answer is correct.
"Assateague is a large island off the coast of Virginia, it is inhabited by wild ponies." This is an example of a run-on sentences. Run-on sentences contain hard stops (longer pauses than a comma would usually indicate in a sentence) and don't contain any transitions, such as "and" or "or". Run-on sentences will never be the answer to these grammar problems (or any problem for that matter), so this answer is incorrect.
"Assateague is a large island off the coast of Virginia: it is inhabited by wild ponies." This is also an incorrect use of punctuation. You would not use a colon here since you're not listing anything off or stating a fact that is a result of your previous statement. Basically, what this sentence is currently indicating is that wild ponies inhabit it because it is a large island off of the coast of Virginia, which is probably not the reason why wild ponies live there. This answer is incorrect.
Your answer will be your first option.
Hope this helped you out! :-)