Artificial Intelligence class hw, i am really lost, if anyone could explain it step by step

Consider the state space search problem shown to the right. A is the start state and the shaded states are goals. Arrows encode possible state transitions, and numbers by the arrows represent action costs. Note that state transitions are directed; for example, A B is a valid transition, but B A is not. Numbers shown in diamonds are heuristic values that estimate the optimal (minimal) cost from that node to a goal. Numbers on lines are costs to reach the next node h of the search algorithms, write down the nodes that are moved from the start state A in the course of the search. After search any one of the three goal states, search is finished. For example, if use Greedy Best-First Search, the answer of the state transitionis "AD Since D is one of the goal state and D has the lowest heuristics function value "0" in the diamond, the search is finished. 3 0 3 .1 Depth-First Search (ignores costs) 4.2 Breadth-First Search (ignores costs) 4.3 A* Search