Explain rules of pericyclic

The pericyclic selection rules say absolutely nothing about the position of equilibrium in every case.  These rules refer to rates of reactions, not to equilibrium constants.  Other considerations must be used to decide on the position of equilibrium.  The point of the problem is for you to use what you have learned about the relative energies of molecules; the molecule of lower energy is favored in each equilibrium.

(b) The left side of the equation is favored at equilibrium because the double bonds have more alkyl branches.  (Alkyl substitution stabilizes a double bond.)

(d) The right side of the equation is favored at equilibrium because single product is aromatic and thus particularly stable, and the other product is volatile (ethylene is a gas)