To find the sum \( 12 \sqrt[3]{3} + (-16 \sqrt[3]{3}) \), we can first rewrite it as:
\[ 12 \sqrt[3]{3} - 16 \sqrt[3]{3} \]
Now, we can factor out \( \sqrt[3]{3} \):
\[ (12 - 16) \sqrt[3]{3} \]
Calculating \( 12 - 16 \):
\[ 12 - 16 = -4 \]
So, we have:
\[ -4 \sqrt[3]{3} \]
Thus, the sum is:
\[ \boxed{-4 \sqrt[3]{3}} \]