Only walls A and C are possible.

On the left, a brick of the original wall is marked in red. It is the vertex of an inverted triangle reaching the top row: those yellow bricks are exactly the ones that must be removed before the red one. On the right, the red brick of the new wall is the vertex of a triangle pointing upwards (cut off at the side): all those yellow bricks must be placed before the red one.

With this idea of triangles it can be checked that A and C are possible. Below, one construction of each is shown (there are many others); the numbers indicate the order in which each brick is moved. The rules are satisfied because: 1) in the original wall, all the bricks of each brick's inverted triangle have a smaller number; 2) in the new wall, all the bricks of each brick's upward triangle have a smaller number.

B is impossible. Think of the moment when the 4th B brick is about to be removed from the original wall. At that moment none of the bricks in the bottom two rows are available, so at most the 4 A bricks and 2 C bricks of the top three rows have been moved. But to place that 4th B brick in wall B, at least 5 A bricks or 3 C bricks must already be in the new wall: a contradiction.

D is impossible. When the 3rd B brick is about to be removed from the original, at least 2 A bricks have already been removed. The second of them must go to the left end of the middle row of wall D (the other A in that row would require the 3rd B to be placed). Now think of the moment the 3rd A brick has just been placed: it must be the second A of the third row (the other options, the left bricks of the top row, require moving 3 C bricks, which cannot happen until 4 A bricks have been removed). So the 2nd and 3rd A go in the middle row, and for that 4 B bricks must already be in the two bottom rows. But to remove 4 B bricks from the original, at least 3 A bricks must be removed first. This contradiction shows that D is impossible.