To find the sum of the product of -8 and -9 and the product of -10 and 12, we will first calculate each product separately.
- Calculate the product of -8 and -9:
\[ -8 \times -9 = 72 \]
- Calculate the product of -10 and 12:
\[ -10 \times 12 = -120 \]
- Now, we find the sum of the two products:
\[ 72 + (-120) = 72 - 120 = -48 \]
Thus, the final result is:
\[ \boxed{-48} \]