Find the set of real value(s) of `a` for which the equation `|2x+3|+|2x-3|=a x+6` has more than two solutions.

Explanation

To solve the equation \( |2x + 3| + |2x - 3| = ax + 6 \) for the values of \( a \) such that it has more than two solutions, we will analyze the equation by considering the different cases based on the values of \( x \).

### Step 1: Identify critical points
The critical points occur where the expressions inside the absolute values are zero:
1. \( 2x + 3 = 0 \) gives \( x = -\frac{3}{2} \)
2. \( 2x - 3 = 0 \) gives \( x = \frac{3}{2} \)

These points divide the number line into three intervals:
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