Supposing I have a multiple regression population function of the form:
$$Y_{i}=\beta_{1}+\beta_{2}X_{2i}+\beta_{3}X_{3i}+u_{i}$$ with $X_{3i}$ a dummy variable (only takes values $0$ and $1$).
I am given a sample of points. Although the latter takes place in 3 dimensional space, the question states "its results can be represented in $Y$ vs $X_{2}$ space". I don't understand how graphing $Y$ vs $X_{2}$ will give us a 2 dimensional representation of our population regression function. Isn't $X_{3i}$ being completely omitted?
Assuming that I properly understand your problem, you have $$Y=\beta_{1}+\beta_{2}X_{2}+\beta_{3}X_{3}$$ where $X_3$ is a binary variable.
This means $$X_3=0 \implies Y=\beta_{1}+\beta_{2}X_{2}$$ $$X_3=1 \implies Y=(\beta_{1}+\beta_{3})+\beta_{2}X_{2}$$ and then, the two dimensional representation of the function (two parallel lines).