To find the y-intercept of a graph, we look for the point where the graph crosses the y-axis. On the y-axis, the value of x is always 0. Therefore, to find the y-intercept of an equation, we substitute 0 for x and solve for y.
Here's a step-by-step solution for finding the y-intercept of the equation \( y = 2(x + 3)(x - 4) \):
Step 1: Substitute \( x = 0 \) into the equation:
\[ y = 2(0 + 3)(0 - 4) \]
Step 2: Simplify the equation using the substituted value:
\[ y = 2(3)(-4) \]
Step 3: Multiply the values to solve for y:
\[ y = 2 \times 3 \times -4 \]
\[ y = 6 \times -4 \]
\[ y = -24 \]
Therefore, the y-intercept of the graph of the equation \( y = 2(x + 3)(x - 4) \) is the point (0, -24).