Find the Thevenin equivalent with respect to terminals a and b in the following circuit. (Items in Blue were added to assist in the solution.)

Since there are no independent sources, the Thevenin Equivalent is simply a resistor.
Since there is a dependent source, we must hook up a test source and determine its effect in order to calculate the equivalent resistance.

I will choose to connect a 1 amp source and use mesh analysis to determine the voltage developed across the circuit.

Define i_D in terms of the mesh currents.

i_D = I_C - I_B

Express the current source in terms of the mesh currents.

I_C = - 1

Removing the current source from the circuit opens mesh C to the external world, so no KVL is needed around mesh C.

Writing KVL around meshes 1 and 2 gives:

Mesh A:

60 I_A + 20 (I_A - I_C) + 16 (I_A - I_B) = 0
96 I_A - 16 I_B - 20 I_C = 0

But I_C = -1, so

96 I_A - 16 I_B = - 20 (equation 1)

Mesh B:

16 (I_B - I_A) + 80(I_B - I_C) - 40 i_D = 0
16 (I_B - I_A) + 80(I_B - I_C) - 40 (I_C - I_B) = 0
- 16 I_A + 136 I_B - 120 I_C = 0

and since I_C = - 1

- 16 I_A + 136 I_B = - 120 (equation 2)

Solving the two equations gives

I_A = - 362.5 mA
I_B = - 925 mA

Writing KVL around mesh C will now yield V

20 (I_C - I_A) + V + 80 (I_C - I_B) = 0
- 20 I_A - 80 I_B + 100 I_C + V = 0
V = 20 (- 362.5 m) + 80 (- 925 m) - 100 (-1)
V= 18.75 V

and since the equivalent resistance equals the voltage developed divided by the value of the current source (1 A), then

R_Th = 18.75 W