In the following circuit diagram, when $3 \Omega$ resistor is removed, then equivalent resistance of the network

The equivalent Wheatstone's bridge network of the given circuit is shown in figure. Here, The points $B$ and $D$ are at the same potential as the bridge is balanced. So, the $3 \Omega$ resistance in $B D$ arm is ineffective and can be omitted from the circuit. Hence, equivalent resistance remains same when $3 \Omega$ resistor is removed.