For the LED to be forward biased and glow, its anode (P) must be at logic 1 (high potential) and cathode (Q) at logic 0 (low potential).

Tracing the top sub-circuit (two cascaded bubble gates implementing an AND from $A,B$): $P=A\cdot B$. So $P=1$ requires both $A=1$ and $B=1$.

Tracing the bottom sub-circuit (a NOR of $C,D$): $Q=\overline{C+D}$. So $Q=0$ requires at least one of $C,D$ to be 1.

Option (4) 1101 gives $A=1,B=1,C=0,D=1$: $P=1\cdot 1=1$ and $Q=\overline{0+1}=0$. LED glows.