From the reaction you can state the molar ratios:
3 mol A : 5 mol B : 1 mol C : 2 mol D : 1 mol E.
Given that B and C are in excess, you know that reactant A is the limiting reactant, which means that is reacts completely. So, you can use the number of moles of reactant B to find how many moles of the products are produced.
For that, you build a proportion with the molar ratios between A and E, and the number of moles of A that reacted:
=> 3 mol A / 1 mol E = 6 mol A / x => x = 6 mol A * 1 mol E / 3 mol A
=> x = 6*1/3 mol E = 2 mol E.
Answer: 2 moles of E.
