The BDD is not split at all. The two BDDs given in the solution are on the left hand side the BDD that contains the conjunction of the variables a,b, that we should quantify over, and the BDD on the right hand side is the result of the existential quantification.

How the existential quantification is computed is shown in detail below the figures. There is a recursive algorithm Exists that is given the two BDDs and that computes the BDD shown on the right hand side in the solution as shown by the recursive calls below those figures. Take some time and study the algorithm you find in the lectures notes before looking at the solution given here. I hope my explanations above gave some orientation for this.