1. **State the problem:** Convert the mixed number $5 \frac{4}{6}$ to an improper fraction. 2. **Formula:** To convert a mixed number $a \frac{b}{c}$ to an improper fraction, use: $$\text{Improper fraction} = \frac{a \times c + b}{c}$$ 3. **Apply the formula:** Here, $a=5$, $b=4$, and $c=6$. $$5 \times 6 + 4 = 30 + 4 = 34$$ 4. **Write the improper fraction:** $$\frac{34}{6}$$ 5. **Simplify if possible:** Both numerator and denominator can be divided by 2. $$\frac{\cancel{34}^{17}}{\cancel{6}^{3}} = \frac{17}{3}$$ 6. **Final answer:** The mixed number $5 \frac{4}{6}$ as an improper fraction is $\frac{34}{6}$ or simplified $\frac{17}{3}$. The correct choice from the options given is $\frac{34}{6}$.