I have a question that is giving me a bit of a hard time, here it is

Consider the problem of finding a path in the grid shown in Figure Ass-1 from the position s to
the position g. A piece can move on the grid horizontally or vertically, one square at a time. No
step may be made into a forbidden shaded area.
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a) On the grid shown in Figure Ass1.1, number the nodes expanded (in order) for a depth-
first search from s to g, given that the order of the operators is up, left, right, and down.
Assume there is cycle pruning. What is the first path found?
b) Using best-first search, nodes are expanding from s to g. Manhattan distance should be
used as the evaluation function. The Manhattan distance between two points is the
distance in the x-direction plus the distance in the y-direction. It corresponds to the
distance travelled along city streets arranged in a grid. Assume multiple-path pruning.
What is the first path found?
c) Using heuristic depth-first search from s to g, the Manhattan distance should be used as
the evaluation function. Assume cycle pruning. What is the path found?
d) Number the nodes in order for an A∗ search, with multiple-path pruning, for the same
grid. What is the path found?
e) Based on this experience, discuss which algorithms are best suited for this problem.

so for A i approached it like this
enter image description here

D A * search
enter image description here

However B and C I am not too sure how to progress as I don’t know how A is different from C and How to go about B. Also if I have made a mistake on the ones I have answered please feel free to correct me. Kind regards