To perform the indicated operation, we start with the expression:
\[ 4 \sqrt{3} \times 11 \sqrt{4} \]
First, we can simplify \(\sqrt{4}\):
\[ \sqrt{4} = 2 \]
Now we can rewrite the expression:
\[ 4 \sqrt{3} \times 11 \times 2 \]
Next, we can combine the coefficients:
\[ 4 \times 11 \times 2 = 88 \]
Now, we can write the expression as:
\[ 88 \sqrt{3} \]
Thus, the final answer is:
\[ \boxed{88 \sqrt{3}} \]