Look at this product pattern:
\(3~\times~4~=~12\)
\(3~\times~(-4)~=~-12\)
\((-3)~\times~4~=~-12\)
What is \((-3)~\times~(-4)\)?
What this problem is really about
The absolute values of the factors stay three and four in every row, so the product’s magnitude never changes. Track only how the sign pattern changes: one negative factor produces a negative product, while matching factor signs produce a positive one. Apply that relationship to the final row without altering the underlying multiplication fact.