1. **State the problem:** Simplify the expression $12 \cdot 2 \left(\frac{3}{5}\right)^2$. 2. **Recall the order of operations:** First, calculate the exponent, then multiplication. 3. **Calculate the exponent:** $$\left(\frac{3}{5}\right)^2 = \frac{3^2}{5^2} = \frac{9}{25}$$ 4. **Substitute back into the expression:** $$12 \cdot 2 \cdot \frac{9}{25}$$ 5. **Multiply the constants:** $$12 \cdot 2 = 24$$ 6. **Multiply 24 by $\frac{9}{25}$:** $$24 \cdot \frac{9}{25} = \frac{24 \cdot 9}{25} = \frac{216}{25}$$ 7. **Simplify the fraction if possible:** 216 and 25 have no common factors other than 1, so the fraction is in simplest form. **Final answer:** $$\frac{216}{25}$$