Circuit Theory/TheveninNorton
Vth using Node
editIn using Node
editRth or Rn
editFinding Rth using source injection and node
edit
zero sources to find Rth

add source injection since parallel/series combinations do not exist

redraw up and down before solving
Here is the mupad/matlab code that generates the answer R_{th} = 6.0591 ohms.
Comparing Node with Thevenin Equivalent
editSolving the node equations yields:
Using the Thevenin equivalent (and voltage divider) to compute voltage across the 12 ohm resistor:
So they match ...
Thevenin voltage and resistance can not be computed from a node analysis of the entire circuit, but the node analysis of the entire circuit can be used to check if the thevenin equivalent produces the same numbers.