What is the thevenin equivalent?
There are plenty of ways to determine the parameters you want. I like to use superposition, especially with controlled sources. Unlike the popular belief, superposition works with controlled sources as described here. The trick is to determine the controlling variable first, \$I_x\$ in your case. When applying superposition, sources (controlled or independent) must alternatively be reduced to 0:a 0-A current source becomes an open circuit while a 0-V voltage source becomes a short circuit. However, when setting a controlled source to 0, its controlling variable is kept untouched. See the below sketch to determine the controlling current \$I_x\$:

From the upper sketch, you have \$I_x=\frac{V_1}{R_1+R_2+R_3}\$. From the lower sketch, you set the 12-V source to 0 and end up with a simple configuration in which you can apply the current divider law: \$I_x=1.5I_x\frac{R_1}{R_1+R_2+R_3}\$. Now sum these two expressions and solve for \$I_x\$. You should find \$I_x=\frac{V_1}{R_2-0.5R_1+R_3}\$. With your values, you have 1.333 A. Having determined \$I_x\$, you see that \$V_{th}=I_xR_3=1.333\;A\times8\;\Omega=10.667\;V\$.
The short-circuit current is also determined using a similar approach:

Applying superposition, we have: \$I_x=\frac{V_1}{R_1+R_2}+1.5I_x\frac{R_1}{R_1+R_2}\$. Solving for \$I_x\$ and realizing that \$I_x\$ is actually your short-circuit current, you have: \$I_{sc}=\frac{V_1}{R_2-0.5R_1}=12\;A\$. The Thévenin output resistance is thus \$R_{th}=\frac{V_{th}}{I_{sc}}=\frac{10.667}{12}=0.889\;\Omega\$. The equivalent circuit is thus drawn as follows:


The calculation file is here:

I have simulated the circuit to obtain the dc operating point. The output impedance requires a dynamic approach by connecting a 1-A current source across \$R_3\$ and using a .TF command:


The superposition theorem applied to dependent sources is really cool. The thing is to understand that the controlling variable, \$I_x\$ in your example, must NOT be set to 0 during superposition. It is the controlled source that is 0. The controlling variable must first be evaluated before proceeding with the calculations. You have videos on YouTube showing how to apply the extension of the original superposition theorem.