1. **State the problem:** Simplify and solve the expression $$\frac{(4x - 7)^2 \cdot (x - 3)(x - 2y)0}{x - 2y4}$$ given the vertical fraction and terms. 2. **Analyze the expression:** The numerator contains $(4x - 7)^2$ multiplied by $(x - 3)$ and $(x - 2y)$ and then multiplied by 0. 3. **Important rule:** Any expression multiplied by 0 equals 0. 4. **Simplify the numerator:** $$ (4x - 7)^2 \cdot (x - 3) \cdot (x - 2y) \cdot 0 = 0 $$ 5. **Rewrite the entire fraction:** $$ \frac{0}{x - 2y4} = 0 $$ 6. **Conclusion:** Regardless of the denominator (as long as it is not zero), the entire expression equals 0. **Final answer:** $$0$$