1. **Problem:** Calculate $12 - \left(\frac{8}{5} + 3 \div \frac{2}{3}\right)$ using BODMAS rules. 2. **Step 1:** Understand BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction). 3. **Step 2:** Evaluate inside the brackets first: $\frac{8}{5} + 3 \div \frac{2}{3}$. 4. **Step 3:** Division inside the bracket: $3 \div \frac{2}{3} = 3 \times \frac{3}{2} = \frac{9}{2}$. 5. **Step 4:** Add fractions inside the bracket: $\frac{8}{5} + \frac{9}{2} = \frac{16}{10} + \frac{45}{10} = \frac{61}{10}$. 6. **Step 5:** Substitute back: $12 - \frac{61}{10} = \frac{120}{10} - \frac{61}{10} = \frac{59}{10}$. 7. **Final answer:** $\frac{59}{10}$ or $5.9$.