\[6\sqrt[4]{7\frac{58}{81}} + 4\sqrt[3]{- 3\frac{3}{8}} = 6\sqrt[3]{\frac{625}{81}} + 4\sqrt[3]{- \frac{27}{8}} =\]
\[= 6 \cdot \frac{5}{3} + 4 \cdot \left( - \frac{3}{2} \right) = 10 - 6 = 4.\]