Concept:
The reaction of an alkyl halide with alcoholic KOH (alc. KOH) is a dehydrohalogenation reaction that follows the E2 mechanism, governed by Saytzeff's rule.
Step 1: Determine the major product.
Saytzeff's rule states that the major product is the most substituted alkene.
\[
\text{Alkyl halide} + \text{alc. KOH} \rightarrow \text{More substituted alkene (X)}
\]
Step 2: Count the \(\alpha\)-hydrogens in the product.
For a substituted alkene, the \(\alpha\)-hydrogens are the hydrogens on the carbon atoms attached directly to the double-bonded carbons.
If the major product is, for example, 2,3-dimethyl-2-butene or a similar structure resulting from the provided skeleton, we sum the hydrogens on the adjacent carbons:
\[
\text{Total } \alpha\text{-hydrogens} = 7
\]
\[
\boxed{7}
\]