The given solution is correct:
The order of the edges added by Dijkstra will be:
1. AB [since the cost is two]
The choice is now have is between four, seven and 12. We choose four.
2. BD [since the cost is four]
The choice is between six, seven and 12.
3. DF [since the cost is six]
The choice is between eight, seven and 12.
4. AC [since the cost is seven]
The choice is between eight and nine.
5. FG [since the cost is eight]
The choice left is nine.
6. CE [since the cost is nine]
I hope this makes sense.