How does the round function in this particular Feistel cipher work?
It seems to me that the exercise is missing some context (which is presumably to be found in the textbook it's taken from).  Specifically, it defines a function $$f: \{0,1\}^4 \times \{0,1\}^4 \to \{0,1\}^4,$$ but does not explicitly state what role this function is supposed to play in the Feistel encryption process.

That said, the usual way to define a Feistel encryption round (as given e.g. on Wikipedia) is $$\begin{aligned} L_{i+1} &amp;= R_i, \\ R_{i+1} &amp;= L_i \oplus F(R_i, K_i), \end{aligned}$$ where $L_i$ and $R_i$ are the left and right halves of the input block to encryption round $i$, $K_i$ is the $i$-th round subkey, and $F$ is some nonlinear function.

Presumably, the function $f$ defined in the exercise corresponds to the nonlinear round function that I've denoted by $F$ above.  Thus, presumably, one of its arguments is supposed to be the round subkey, while the other one is one of the input half-blocks, just like you say.  However, what's not obvious from the given definition is which argument is supposed to be the subkey, or whether the other argument is supposed to be the left or the right half-block (since either convention can be used, and they're essentially equivalent).

Anyway, if the exercise comes with an answer sheet, it should be easy enough to verify this just by doing the encryption is each of the possible ways and comparing the results with the expected answer.  Even with the small block size, getting the right answer just by change from the wrong encryption process should be pretty unlikely.