1. **State the problem:** Calculate the value of $10 - \frac{2}{3} \times 6$. 2. **Recall the order of operations:** Multiplication and division are performed before addition and subtraction. 3. **Calculate the multiplication first:** $$\frac{2}{3} \times 6 = \frac{2 \times 6}{3} = \frac{12}{3}$$ 4. **Simplify the fraction:** $$\frac{12}{3} = \cancel{\frac{12}{3}} = 4$$ 5. **Substitute back into the expression:** $$10 - 4$$ 6. **Perform the subtraction:** $$10 - 4 = 6$$ **Final answer:** $6$