imc

In order for $a\cdot d-b\cdot c$ to be odd, consider parity. We must have (even)-(odd) or (odd)-(even). There are $2(2+4)=12$ ways to pick numbers to obtain an even product. There are $2\cdot 2=4$ ways to obtain an odd product. Therefore, the total amount of ways to make $a\cdot d-b\cdot c$ odd is $2\cdot (12\cdot 4)=\boxed{96}$.