1. The problem is to evaluate the expression $4 \div \frac{2}{3}$. 2. When dividing by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. 3. So, $4 \div \frac{2}{3} = 4 \times \frac{3}{2}$. 4. Multiply the numerator and denominator: $$4 \times \frac{3}{2} = \frac{4 \times 3}{2} = \frac{12}{2}$$. 5. Simplify the fraction by dividing numerator and denominator by 2: $$\frac{\cancel{12}^{6}}{\cancel{2}^{1}} = 6$$. 6. Therefore, the final answer is $6$.