1. **State the problem:** Simplify the expression $6 - \frac{4^2}{6} + 4^2$. 2. **Recall order of operations:** We must evaluate exponents first, then division and multiplication from left to right, and finally addition and subtraction from left to right. 3. **Calculate exponents:** $$4^2 = 16$$ 4. **Substitute back:** $$6 - \frac{16}{6} + 16$$ 5. **Perform division:** $$\frac{16}{6} = \frac{8}{3}$$ 6. **Rewrite expression:** $$6 - \frac{8}{3} + 16$$ 7. **Convert whole numbers to fractions with denominator 3:** $$6 = \frac{18}{3}, \quad 16 = \frac{48}{3}$$ 8. **Combine all terms:** $$\frac{18}{3} - \frac{8}{3} + \frac{48}{3} = \frac{18 - 8 + 48}{3} = \frac{58}{3}$$ 9. **Final answer:** $$\boxed{\frac{58}{3}}$$