= Solution
Filling the three <bonding molecular orbitals> with two <electrons> each gives
$$
E_\pi=2(\alpha+2\beta)+4(\alpha+\beta)=6\alpha+8\beta.
$$
Three isolated ethene-like $\pi$ bonds, evaluated with the same <Hückel method> parameters, have $E_{\rm loc}=3\{2(\alpha+\beta)\}=6\alpha+6\beta$. Thus the signed <delocalization energy> is
$$
\boxed{\Delta E=E_\pi-E_{\rm loc}=2\beta<0.}
$$
Equivalently, the positive stabilization is \b[$-2\beta=2|\beta|$].
<Benzene> has a planar cyclic <conjugated system> with six $\pi$ <electrons>, satisfying the $4n+2$ count with $n=1$. All three bonding $\pi$ <molecular orbitals> are filled and the antibonding levels are empty, giving the closed-shell stabilization associated with <aromaticity>. The conclusion uses the continuous cyclic overlap as well as the <electron> count.
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