1. **Problem:** Calculate $5 \frac{1}{3} \times \frac{12}{10} \div 0.6$. 2. **Step 1:** Convert mixed number to improper fraction: $$5 \frac{1}{3} = \frac{16}{3}$$ 3. **Step 2:** Write the expression with fractions: $$\frac{16}{3} \times \frac{12}{10} \div 0.6$$ 4. **Step 3:** Convert decimal to fraction: $$0.6 = \frac{6}{10} = \frac{3}{5}$$ 5. **Step 4:** Division by a fraction is multiplication by its reciprocal: $$\frac{16}{3} \times \frac{12}{10} \times \frac{5}{3}$$ 6. **Step 5:** Multiply numerators and denominators: $$\frac{16 \times 12 \times 5}{3 \times 10 \times 3} = \frac{960}{90}$$ 7. **Step 6:** Simplify the fraction by canceling common factors: $$\frac{\cancel{960}^{32 \times 30}}{\cancel{90}^{3 \times 30}} = \frac{32}{3}$$ 8. **Step 7:** Convert improper fraction to mixed number: $$\frac{32}{3} = 10 \frac{2}{3}$$ **Final answer:** $10 \frac{2}{3}$