The number of hyperconjugation structures involved to stabilize carbocation formed in the above reaction is…

In the first step of the reaction, protonation of alcohol takes place and carbocation is formed after removal of water. The carbocation formed undergo rearrangement to get stability. In the given, methyl shift takes place to convert secondary carbocation to tertiary carbocation. The alpha hydrogen to the positive charged carbon are involved in hyperconjugation.

So, number of hyperconjugation structures in most stable carbocation

$= 6 + 1 = 7$