Dijikstra's algorithm should have traverse minimum weight of path. So we can derive like below from above graph through given optional,
(a){a,d,c,f,g} ={6(initial weight) + 2 + 3 + 1} = 12
(b){a,b,d,c,f,g} = {3(initial weight) + 2 + 2 + 3 + 1} = 11
(c){a,c,g} = {5(initial weight) + 7} = 12
(d){a,c,f,g} = {5(initial weight) + 3 + 1} =9
So answer is B.
Note: if same weight available in a graph ,at that time we shall take minimum value of initial node will take as followed by next node to destination.