Question: if $2(b - 6)\3 = 4$, what is the value of $b - 6$
1. **State the problem:** We need to find the value of $b - 6$ given the equation $2(b - 6)\3 = 4$.
2. **Rewrite the equation:** The expression $2(b - 6)\3$ means $\frac{2(b - 6)}{3} = 4$.
3. **Use the formula:** To solve for $b - 6$, multiply both sides of the equation by 3 to eliminate the denominator:
$$\cancel{3} \times \frac{2(b - 6)}{\cancel{3}} = 4 \times 3$$
which simplifies to:
$$2(b - 6) = 12$$
4. **Divide both sides by 2:**
$$\frac{2(b - 6)}{\cancel{2}} = \frac{12}{\cancel{2}}$$
which simplifies to:
$$b - 6 = 6$$
5. **Final answer:** The value of $b - 6$ is $6$.