Your solution is correct! You have applied the product rule of exponents correctly by adding the exponents of the same base:
\[ 12^{-5} \cdot 12^{7} = 12^{-5 + 7} = 12^{2}. \]
Then you correctly computed \( 12^{2} \) as follows:
\[ 12^{2} = 12 \times 12 = 144. \]
Thus, the final answer is indeed \( 144 \). Great job!