1. **State the problem:** We need to add the mixed numbers $-4 \frac{3}{8}$ and $6 \frac{1}{3}$. 2. **Convert mixed numbers to improper fractions:** $-4 \frac{3}{8} = -\left(4 + \frac{3}{8}\right) = -\frac{32}{8} - \frac{3}{8} = -\frac{35}{8}$ $6 \frac{1}{3} = 6 + \frac{1}{3} = \frac{18}{3} + \frac{1}{3} = \frac{19}{3}$ 3. **Find a common denominator:** The denominators are 8 and 3. The least common denominator (LCD) is 24. 4. **Convert fractions to have the LCD:** $-\frac{35}{8} = -\frac{35 \times 3}{8 \times 3} = -\frac{105}{24}$ $\frac{19}{3} = \frac{19 \times 8}{3 \times 8} = \frac{152}{24}$ 5. **Add the fractions:** $-\frac{105}{24} + \frac{152}{24} = \frac{-105 + 152}{24} = \frac{47}{24}$ 6. **Convert the improper fraction back to a mixed number:** $\frac{47}{24} = 1 \frac{23}{24}$ 7. **Final answer:** $-4 \frac{3}{8} + 6 \frac{1}{3} = 1 \frac{23}{24}$