An ordinary 6-sided die has a number on each face from 1 to 6 (each number appears on one face). How many ways can I paint two faces of a die blue, so that the product of the numbers on the painted faces isn't equal to 4?

You can paint it the following number of ways:

(3 and 1), (1 and 3), (2 and 1), (1 and 2) ==4 different ways.