1. **State the problem:** Calculate the product of $6$ and $\frac{2}{3}$. 2. **Formula used:** Multiplication of a whole number by a fraction is done by multiplying the whole number by the numerator and then dividing by the denominator. 3. **Intermediate work:** $$6 \times \frac{2}{3} = \frac{6 \times 2}{3} = \frac{12}{3}$$ 4. **Simplify the fraction:** $$\frac{12}{3} = 4$$ 5. **Explanation:** Multiplying $6$ by $\frac{2}{3}$ means taking two-thirds of $6$. We multiply $6$ by $2$ to get $12$, then divide by $3$ to get $4$. So, the final answer is $4$.