1. The problem is to multiply the mixed numbers $4 \frac{1}{4}$ and $-1 \frac{1}{3}$. 2. First, convert the mixed numbers to improper fractions. $$4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{17}{4}$$ $$-1 \frac{1}{3} = -\frac{1 \times 3 + 1}{3} = -\frac{4}{3}$$ 3. Now multiply the two improper fractions: $$\frac{17}{4} \times -\frac{4}{3} = \frac{17 \times \cancel{4}}{\cancel{4} \times 3} \times -1 = -\frac{17}{3}$$ 4. Simplify the fraction if possible. Here, $-\frac{17}{3}$ is already in simplest form. 5. Convert the improper fraction back to a mixed number: $$-\frac{17}{3} = -5 \frac{2}{3}$$ 6. Final answer: $$4 \frac{1}{4} \times -1 \frac{1}{3} = -5 \frac{2}{3}$$