1. **State the problem:** Evaluate the expression $-3(-11+2\times4)^2$. 2. **Apply order of operations:** First, calculate inside the parentheses and perform multiplication before addition. 3. Calculate $2\times4=8$. 4. Substitute back: $-11+8 = -3$. 5. Now the expression is $-3(-3)^2$. 6. Square $-3$: $(-3)^2 = 9$. 7. Multiply by $-3$: $-3 \times 9 = -27$. **Final answer:** $-27$.