Two discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected incascade.
The overall impulse response of the cascaded system is

δ[n - 1] + δ[n - 2]
 
δ[n - 4]
 
δ[n - 3]
 

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