"Only we like the fourth one."
Translation:Csak mi szeretjük a negyediket.
Just to clarify: using csak as "but" is contextual. It's used like this when you want to want to say why the actions in the first half of the sentence couldn't achieve their goal completely. In this sense, it's similar to th English "only to", like in "They survived only to die."
Elmentem a bolthoz, csak zárva volt. = I went to the shop but it was closed.
Here what is meant is that "I went to the shop to buy some stuff, but I couldn't buy stuff because it was closed."
"A lemezen a harmadik film volt, csak mi a negyediket szeretjük."
All explanations are clear to me, ie how only and but are related. Only/But how it applies to the original sentence with the proposed different word order, I don't get that.
The fourth one is only liked by us. No idea how to create even a first and second part, it is just one statement, and so I fail to see how a but can be meant here.