Concept used

The number of hyperconjugative structures stabilizing a carbocation equals the number of $\alpha$-hydrogen atoms present on the carbon atom(s) adjacent to the positively charged carbon.

Carbocation formed

In the given reaction, the carbocation formed is the tert-butyl carbocation:

$(CH_3)_3C^+$

Here, the positively charged carbon is attached to three methyl groups.

Count the $\alpha$-hydrogens

Each adjacent methyl group, $CH_3$, contributes 3 hydrogens.

So total $\alpha$-hydrogens are:

$3 + 3 + 3 = 9$

Hyperconjugative structures

For carbocations, each $\alpha$-hydrogen gives one no-bond resonance (hyperconjugative) structure.

Hence, the number of hyperconjugation structures is:

$9$

Comparison with stored answer

Stored correct answer = $7$

My derived answer = $9$

These do not match.

A value of $7$ would correspond to the convention of counting total canonical forms including the original carbocation structure for a carbocation with $6$ hyperconjugative forms, or it may be due to a different carbocation than the usual tert-butyl case. But for the standard carbocation $(CH_3)_3C^+$, the number of hyperconjugative structures is clearly $9$.