The image/reaction scheme is not visible in the provided prompt, so the actual product structure cannot be derived from the given information alone.

To determine the number of $sp^2$ hybridized carbon atoms, I would need the reactant(s), reagent(s), and/or the product structure shown in the reaction.

Since the prompt includes a stored correct answer of $7$, I cannot independently verify it without the missing reaction figure.

1. $sp^2$ carbons typically occur in:

   • alkenes: each carbon of a $C=C$ bond
   • aromatic rings: each ring carbon in benzene-like systems
   • carbonyl carbons: the carbon of $C=O$

2. But the exact count depends entirely on the product structure.

3. Because the reaction image is missing, a step-by-step derivation is not possible from the supplied data.

Therefore, I cannot honestly derive the answer; I can only note that the stored answer is $7$.