Determine the impulse response of the following discrete system
When the difference equation is given, one can directly read the impulse response from it. 

In your case the difference equation is given as: y[n] = x[n]- 2x[n-2]+ x[n-3]- 3x[n-4]

This means the output is the input + minus twice the input delayed by two samples + the input delayed by three samples... 
Notice, the input delayed one sample has no influence on the output.

When stimulating the input of this LTI system with a unit impulse y[0] = x[0]. All other terms are zero since our input is an impulse which is a dirac at 1 and 0 else. At timepoint 1 y[1] becomes 0, since there is no x[n-1] term. Try to put in 1 for every n. Remember x is zero everywhere except at 0. At timepoint 2 y[2] is -2x[2-2]=-2x[0]=2. Time steps y[3] becomes x[3-3]=x[0]=1 and And for the last term after four steps -3x[4-4]=-3x[0]=-3. After that y is zero.

Conclusion: stimulating the network with a impulse the response becomes h[n] = [1 0 -2 1 -3]. One gets this result quite fast if he takes all coefficients of the delayed x terms.