Can you perform a two-sample t-test with a moderately skewed sample distribution

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This was a question on my AP Stat test that I got wrong and I am not sure if it is correct:

Essentially the question stated you have two samples both of which don't satisfy the large counts condition (their samples are less than 30) and the distribution of their population is unknown. One sample is approximately symmetric and the other sample has moderate skewness. Can you perform a significance test?

I said that you could perform the t-test as both him and our textbook stated that as long as their is no "strong" skewness you can. I feel as this may be a debate over semantics but this question was worth 8 points on our final. Should I ask him about it or is he correct in that you can't perform the test?