How many negative integers when multiplied together give a positive product?

**Same sign → positive.**
$3\times 4=12$ (both positive)
$(-3)\times (-4)=12$ (both negative — still positive)

**Different signs → negative.**
3 × (−4) = −12
(−3) × 4 = −12

**Why two negatives become positive:** think of −3 as 'the opposite of 3'. So $(-3)\times (-4)$ = 'the opposite of $(3\times -4)$' = the opposite of −12 = +12. The double-negative cancels.