Help with Graph search problem

For the next problem I can not think of how to find a solution with graph searches (I thought it was backtraking but my college professor told me that I should use graph searches, which I do not know much about, to solve it).

As input we obtain a matrix (3×4) of connections (“|” or “-“) which we must decode in the least amount of movements, to avoid that the bomb explodes. As an output inform one of the possible solutions.

The decoding consite in that the matrix must contain only characters “-“. To achieve this they tell us that if we move an element of the matrix, both the values ​​of the column and row of the matrix change. For example if I move the element (0,0) of the matrix in this case the “-” change to “|” and vice versa in the column 0 and row 0. In the image (where (1) represents the input matrix and (2) the decoded matrix) a solution to inform would be:

move (0,3) and then (2,1)

enter image description here

How to design an algorithm that solves this problem without using backtraking directly? Thank you in advance