1. **State the problem:** We need to evaluate the expression $$\frac{3 \times 5}{6 - 4 + 3}$$. 2. **Recall the order of operations:** Multiplication and division are performed before addition and subtraction, but since the numerator and denominator are separated by a fraction bar, we first simplify numerator and denominator separately. 3. **Calculate the numerator:** $$3 \times 5 = 15$$. 4. **Calculate the denominator:** $$6 - 4 + 3$$. Perform subtraction and addition from left to right: $$6 - 4 = 2$$ $$2 + 3 = 5$$ 5. **Rewrite the fraction:** $$\frac{15}{5}$$. 6. **Simplify the fraction:** Divide numerator and denominator by their greatest common divisor, which is 5: $$\frac{\cancel{15}^{3} }{\cancel{5}^{1}} = 3$$. 7. **Final answer:** The value of the expression is **3**.