To simplify the expression \(-7\sqrt{3} + 4\sqrt{48}\), we first simplify \(\sqrt{48}\).
\[ \sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3} \]
Now, we substitute \(\sqrt{48}\) back into the original expression:
\[ 4\sqrt{48} = 4 \cdot 4\sqrt{3} = 16\sqrt{3} \]
Now, replace \(4 \sqrt{48}\) in the expression:
\[ -7\sqrt{3} + 16\sqrt{3} \]
Next, combine the terms by adding the coefficients of \(\sqrt{3}\):
\[ (-7 + 16)\sqrt{3} = 9\sqrt{3} \]
Thus, the simplified expression is:
\[ \boxed{9\sqrt{3}} \]