In mux output will depend upon select line, when S = 0, input line 0 will be selected, when select line, S =1, input line 1 will be selected.
Considering S0 = select line of first mux, S1 = select line of second mux.
Case 1 : when T = 0, S0=0 and S1 = 1
Propagation delay= Delay due to input 0 (Nor gate, Since S0=0) + Delay due to MUX1 + Delay due to input 1(Since S1 =1) + Delay due to MUX2
So propagation delay = 2ns + 1.5ns + 0ns+ 1.5ns = 5ns
Case 2 : when T =1, S0 =1 and S1 = 0
Propagation delay = Delay due to input 1 (Not gate, Since S0=1) + Delay due to MUX1 + Delay due to input 0(Nor gate,Since S1 =0) + Delay due to MUX2
So propagation delay = 1ns + 1.5ns + 2ns+ 1.5ns = 6ns
Maximum propagation delay = max(case 1, case 2) = max ( 5ns, 6ns) = 6ns.