The circuit comprises:

Four Recognizers $($RA$,$ RB$,$ RC$,$ RD$)$: These are Mealy machines implemented with state transitions.

Clock Input $($Clk$)$: Ensures synchronous operation.

Logic Gate $($AND Gate$)$: The final output R is the AND of the outputs from RA$,$ RB$,$ RC$,$ and RD$.$

Circuit elements:

RA: Detects $"6".$

RB: Detects $"1".$

RC: Detects $"7".$

RD: Detects $"4$ and #$".$

The outputs of RA$,$ RB$,$ RC$,$ and RD feed into an AND gate, producing output R$.$

The schematic includes:

Four recognizers $($RA$,$ RB$,$ RC$,$ RD$),$ each detecting a part of the sequence.

Clock $($Clk$)$ for synchronization.

AND Gate to combine outputs from all recognizers.

$1$st step:

The AND gate ensures the final output R is $1$ only if all recognizers successfully detect their sequences.