In the given circuit, the equivalent resistance between the terminal A and B is ____ Ω

In the given circuit, both $4 \mathrm{\Omega }$ resistors get shorted out, thus no current will flow from them. Removing the resistors from which no current will flow.

Now, the circuit can be redrawn as shown below.

$R_{\mathrm{eq}}=3+(2\Vert 2)+6$

$\Rightarrow R_{\mathrm{eq}}=3+\frac{2\times 2}{2+2}+6$

$\Rightarrow R_{\mathrm{eq}}=10 \mathrm{\Omega }$