1. **State the problem:** Solve for $M$ in the equation $$-\frac{5}{6} + M = \frac{4}{3}.$$\n\n2. **Isolate $M$:** Add $\frac{5}{6}$ to both sides to get $$M = \frac{4}{3} + \frac{5}{6}.$$\n\n3. **Find common denominator:** The denominators are 3 and 6. The least common denominator is 6. Convert $\frac{4}{3}$ to $\frac{8}{6}$ so we have $$M = \frac{8}{6} + \frac{5}{6}.$$\n\n4. **Add the fractions:** $$M = \frac{8 + 5}{6} = \frac{13}{6}.$$\n\n5. **Final answer:** $$M = \frac{13}{6}.$$\n\nThis matches the third option.