1. The problem statement, all variables and given/known data
I'm trying to find the voltage drop V1 of the following circuit, assuming Vin=1v, and for the life of me can't seem to get the right answer.

Spoiler: Picture of Circuit

2. Relevant equations
KCL, Ohm's law

3. The attempt at a solution
I basically tried to use KCL at the top node,

Code (Text):

Vin/2+2V1 = V1/3 + Vin/6, so 1/2=-2V1+V1/3+V1/6, (1/2)/(1.5)=V1=1/3, but apparently that's the incorrect answer

I don't understand the terms of your node equation. For example, the first term of the LHS (left hand side) is Vin /2. How do you arrive at that? And on the RHS you have Vin/6, but Vin is not the node voltage. Can you explain your reasoning?

Yes, Vin/2 is ohm's law, using input voltage (1v) and the resistance (2ohm) to find the Current through the resistor, and thus the current going into the node. As for the Vin over 6, since the 3ohm and 6ohm resistors are in parallel, they share the same voltage, do they not? This is just ohm's law again, except for the current leaving the node through this branch.

Edit: I didn't get it correct though, so my logic is flawed somewhere...

You need not assume any value for Vin.
You should combine the 3 ohm and 6 ohm resistors in parallel and use their equivalent resistance (for simplicity). You'll still have the two nodes, and three currents instead of four.

Write the KCL (node voltage) equation again and simplify.

Vin is not the potential difference between the two ends of the 2 Ω resistor. Only the left side of that resistor is at potential Vin. What is the potential at its other end? So then what is the potential difference?