Answer:
Both the 1/8 inch button and the 1/4 inch button will fit through the hole.
Explanation:
The easiest way to find this is to turn these into decimals. Any decimal that is smaller than the shirt hole will work.
Shirt hole
2/6 = .333
Buttons
1/8 = .125 (FITS)
3/8 = .375 (DOES NOT)
1/4 = .25 (FITS)