Step 1 :Convert $6 \frac{3}{4}$ into a decimal, which is 6.75.
Step 2 :Calculate the product of 6.75 and -11.5, which is -77.625.
Step 3 :Convert -77.625 into a mixed number, which is $-77 \frac{5}{8}$.
Step 4 :\(\boxed{-77 \frac{5}{8}}\) is the final answer.