I am currently self studying/ self teaching myself this great book Mathematical methods of physics by Mathews and Walker and must tell you that I am really struggling with the explanation of the solution of wave equation given on the book using Green's function from the start to the last, so suggest me the technique used in here to solve this problem

$\displaystyle \nabla^{2}\phi-\frac{1}{c^{2}}\frac{\partial^2 \phi}{\partial x^2}=\delta(x-x')\delta(t-t')$