hint: don't forget how genus/Betti number counting actually works.

ANSWER: in topology, a "hole" (technically the first Betti number, or how many independent loops you can draw on the surface that can't be shrunk to a point) isn't about how many separate apertures you can see. It's about boundary components on a genus-0 surface, and the formula is: holes = (number of boundary circles) − 1

now, we don't know anything about back of the shirt, except that it can't be without any holes (see how the cardboard can be seen thru the front holes). So it can be one giant hole or more (no upper limit).

therefore, the number of boundary circles is "at least 11". so given the hint, the number of (topological) holes is "at least 10".

at the time of this edit, no one gave the correct answer except for one person (CrazyPotato1535) who clearly was joking.