You can treat Block A as a giant pulley because, although Block B rests on it, the motion of Block B does not affect the motion of Block A, since there is no friction between them.  The only forces on Block A are two tension forces in the string.  

So you can imagine that Block B rests on the smooth table, instead of on Block A.  Both Blocks A and B then slide on the smooth table. Block A is attached to the 2 small pulleys, and can be lumped with them into a single pulley which slides to the right, as in Farcher's diagram.  

A word of caution : unlike the pulleys Block A does not rotate, so the "giant pulley" idea could not be used if the rotational KE of the pulleys had to be taken into account.