Finding initial values for linear discrete time systems?

I'm not sure if this is the correct place to post since my class is called Linear Systems and Signals, so sorry if its the wrong place.

Can someone the following steps of this solution for me?

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Mainly how they got their initial conditions? The 7.30 equation is just h[n-m] = bm which doesn't help me much.

For our problem, I know that n=3 and m =1 since the LHS highest degree is +3 and RHS highest degree is +1

then h[3-1] = h[2] = 6 because coefficient b1 which is in front of f[k+1] is 6. At least that is what I think. Correct me if I am wrong.

But then how do they obtain h[1] and h[0]? Why are we plugging in values for K?