1. **State the problem:** Calculate $\frac{1}{3} - \frac{1}{4}$ of $\frac{4}{3}$. 2. **Understand the expression:** The word "of" means multiplication, so the expression is $\frac{1}{3} - \left(\frac{1}{4} \times \frac{4}{3}\right)$. 3. **Calculate the multiplication first:** $$\frac{1}{4} \times \frac{4}{3} = \frac{1 \times 4}{4 \times 3} = \frac{4}{12}.$$ Simplify $\frac{4}{12}$ by canceling common factors: $$\frac{\cancel{4}}{\cancel{12}} = \frac{1}{3}.$$ 4. **Substitute back:** $$\frac{1}{3} - \frac{1}{3}.$$ 5. **Perform the subtraction:** $$\frac{1}{3} - \frac{1}{3} = 0.$$ **Final answer:** $0$