Finding the equivalent inductance across terminals a and b with a wire included
L4 = 10 H is shorted. So it can be removed from the circuit.

You have to calculate parallel inductance of


9 H + 3 H (L2 and L3)
12 H (L5)
6 H (L6)


which is 3 H. Then you add the series 4 H (L1) and you get 7 H equivalent inductance.