1. **State the problem:** Simplify the expression $$\left( \frac{3\sqrt{8}}{2\sqrt{7}} \right)^2$$. 2. **Recall the formula:** When squaring a fraction, square the numerator and the denominator separately: $$\left( \frac{a}{b} \right)^2 = \frac{a^2}{b^2}$$. 3. **Apply the formula:** $$\left( \frac{3\sqrt{8}}{2\sqrt{7}} \right)^2 = \frac{(3\sqrt{8})^2}{(2\sqrt{7})^2}$$. 4. **Square numerator and denominator:** $$ (3\sqrt{8})^2 = 3^2 \times (\sqrt{8})^2 = 9 \times 8 = 72 $$ $$ (2\sqrt{7})^2 = 2^2 \times (\sqrt{7})^2 = 4 \times 7 = 28 $$ 5. **Rewrite the fraction:** $$ \frac{72}{28} $$ 6. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD):** GCD of 72 and 28 is 4. $$ \frac{\cancel{4} \times 18}{\cancel{4} \times 7} = \frac{18}{7} $$ 7. **Final answer:** $$ \boxed{\frac{18}{7}} $$