= Solution
The <Woodward-Hoffmann rules> for a $4n+2$ <electron> <electrocyclic reaction> permit \b[thermal disrotation and photochemical conrotation]. Here six <electrons> <mean> $n=1$. For the ground-state six-electron chain, opposite terminal rotations match the terminal phases of its highest occupied orbital as the closing sigma bond forms. A one-electron excitation changes the relevant occupancy and reverses the allowed rotational mode. Thus A opens conrotatorily under light to the specified B, while B closes disrotatorily on heating. Reversing the rotational mode changes the adjacent methyl relationship from cis to trans, exactly as in C.
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