1. The problem is to simplify the expression $12 - \left( \frac{8}{5} + 3 \div \frac{2}{3} \right)$. 2. Recall the order of operations: parentheses first, then division and multiplication from left to right, and finally addition and subtraction. 3. Inside the parentheses, we have $\frac{8}{5} + 3 \div \frac{2}{3}$. We first perform the division $3 \div \frac{2}{3}$. 4. Dividing by a fraction is the same as multiplying by its reciprocal: $3 \div \frac{2}{3} = 3 \times \frac{3}{2} = \frac{9}{2}$. 5. Now the expression inside the parentheses is $\frac{8}{5} + \frac{9}{2}$. To add these fractions, find a common denominator, which is 10. 6. Convert each fraction: $\frac{8}{5} = \frac{16}{10}$ and $\frac{9}{2} = \frac{45}{10}$. 7. Add the fractions: $\frac{16}{10} + \frac{45}{10} = \frac{61}{10}$. 8. Now the original expression is $12 - \frac{61}{10}$. Convert 12 to a fraction with denominator 10: $12 = \frac{120}{10}$. 9. Subtract: $\frac{120}{10} - \frac{61}{10} = \frac{59}{10}$. 10. The simplified result is $\frac{59}{10}$ or $5.9$.