= Solution
\b[The requested equality is $32$ electrons if each unsaturated $C=CHPh$ unit is counted as a four-electron donor to the chosen extended cluster framework.] It needs that additional convention; a count confined to the localized $\mathrm{Al}_7\mathrm C_5$ skeleton gives $28$ instead.
For $B$, an $\mathrm{AlR}$ fragment contributes two skeletal electrons, a singly substituted cap $\mathrm{CR}$ contributes three, and the bridging hydrogen contributes one:
$$
N_B=8(2)+5(3)+1=32.
$$
For the second formula, let $x$ be the contribution assigned to each unsaturated unit. The comparison is
$$
N=7(2)+3(3)+2x+1=24+2x.
$$
Thus $N=N_B$ requires $x=4$. A bookkeeping partition that includes the two alkene $\pi$ pairs in the extended cluster electron pool gives
$$
N_{\rm extended}=7(2)+3(3)+2(2+2)+1=32.
$$
In contrast, assigning the $C=C$ <double bond> entirely to the exoskeletal substituent leaves each corresponding cage carbon with two electrons for the cage:
$$
N_{\rm localized}=7(2)+3(3)+2(2)+1=28.
$$
The difference is exactly the two $\pi$ pairs, four electrons, rather than an arithmetic discrepancy. These are different electron partitions: \b[do not compare $28$ from one partition with $32$ from the other as though both were the same skeletal count], and do not infer a structural classification merely by inserting the extended count into <Wade's rules> for twelve localized skeletal vertices.
Both the original and revised question pages print the same neutral molecular formula; the revised copy does not supply a charge, a drawing, or an explicit instruction about these $\pi$ electrons.<Revised question 33 of the 2022 Cambridge Part III Chemistry Paper 2>[Part (d)(iii), physical page 81 of the later public bundle; the formula is unchanged from the original question]{ref} The primary study identifies the open cluster with the two genuine $C=C$ groups and reports their <hydroalumination> to give the capped aluminium cube. Its accessible abstract does not establish the orbital partition needed to select the four-electron convention.<New Carbaalanes Containing Clusters of Aluminum and Carbon Atoms by Werner Uhl and others>[Abstract: open cluster 2 and its conversion to compound 4; Organometallics 19 (2000), 4536–4543]{ref}
\b[Conditional conclusion:] the advertised $32$-electron equality follows under the explicit extended-framework convention above. Without evidence that those $\pi$ pairs belong in the cluster electron pool, retain the $28$-electron localized count and this qualification. The source checks do not justify asserting a typo or inventing a charge to force agreement.
\b[TODO:] confirm the intended orbital partition from a complete primary orbital analysis or an authoritative clarification of the question.
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