The system is described with the following recursive differences equation:
$$y[n]-4y[n-1]+4y[n-2]=20x[n]+10x[n-1]$$
now lets say the input is delayed by k, then:
$$y[n]-4y[n-1]+4y[n-2]=20x[n-k]+10x[n-1-k]$$
and now the output by the same k:
$$y[n-k]-4y[n-1-k]+4y[n-2-k]=20x[n-k]+10x[n-1-k]$$
here is the problem , I cannot see how same expression will be acquired . I've tried performing simple substitution of n-k=m , which leads to:
$$y[m]-4y[m-1]+4y[m-2]=20x[m]+10x[m-1]$$
which is still not quite the same. Obviously the equation is linear differences equation with constant coefficients , therefore I suppose the system indeed TI but how to mathematically show this specific case.