Let me try to help the reader not quite motivated, probably by lack of techniks.
When you try to resolve a very simple standard draughts problem I guess you do not try all moves until you find, by chance, the solution.
Black to play
For example in the above diagram I guess you first notice the hole in 37 and 26, then you note that black piece on 19 may be able to do a capture move using these holes and after that you can easily find the solution.
For a retrograde problem it is exactly the same; you cannot try all possibilties hoping to find by chance the solution.
Supposing you do not have a solution without capture I will try here to show you how to find a 2 plies retrograde problems with two examples.
From the initial position, which, per definition, has to be a stable position, we are then searching a quiet white ply (no capture) followed by a black capture ply.
We are then searching in particular a white piece (for the first quiet move of the sequence) and a black piece (for the second ply which is a capture move).
When comparing the initial position (the position we are searching) and the final position (i.e. the problem proposed) you can observe that one black piece has changed its place and some white pieces have been added (the captured pieces).
If you search a 2 plies solution that means that one of the two black men on 20 and 30 do a capture ply, and this capture move is preceded by a quiet white ply from a stable position.
Let's first eliminate a capture with the black man on 30.
If you suppose a capture ending in 30 that means that the black man on 20 is still in 20 in the initial position and because the initial position is stable you are forced to put two white pieces on 9 and 14 in the initial position.
Because the capture by black 30 cannot take a white piece on 9 you can easily conclude that the white piece on 9 is necessarily the origin of the first white move and the white piece on 14 has to be captured by the black piece on 30
When you look and the working diagram above you can see the capture ply by black could only begin from square 10 but this is impossible because on 10 black man is unstable.
Now we know that the capture ply has to be done by the black piece on 20.
In the same way you can deduce that, in the initial position, you must have 2 white pieces on 34 and 39. The first white move has to be done by white pieces on 39 (I draw it as a king to remember that this piece has to do the first ply)
Now you have only to retrograde a capture ply from black 20, including the capture of white man on 34 and avoiding any unstablity.
if you suppose a capture from black 10 you reach the working diagram
and you cannot see any solution because from the square 41 the retrograde capture has to put a white man on 37 and the resulting position wil not be stable.
The only possibility (for a 2 plies solution) is to take the black man 42 for the capture ply. To reach a stable position you need now to put piece on square 36. This cannot be the origin square of the black 42 and this cannot be a white piece that can be captured. The piece on square 36 is necessarily a white piece which will do the first ply in order to provoque the capture ply.
First working diagram
Now what could be the origine square of black 42 for its capture ply. Because the capture is provoked by a move from white piece on 36 the only solution for this square is 4.
Second working diagram
The first move of the solution is 36-9 and the final capture is obvious isn't it?
I do not know if my explanations are clear but keep in mind that simple reasonning may greatly help you by avoiding inefficient searches.