 Solution

The six pi electrons of B reorganize in a concerted electrocyclic reaction: the two terminal p orbitals form the new sigma bond, and the other two pi bonds shift to give the conjugated cyclohexadiene. Thermal six-electron closure is disrotatory, so the termini rotate in opposite senses. Applied to the terminal configurations drawn for B, this gives the trans methyl relationship. There is no need to invoke a radical chain or a sigmatropic transfer of a methyl group.