Answer :
Recall the following rules for operating with vectors:
[tex]\begin{gathered} \langle x_A,y_A\rangle+\langle x_B,y_B\rangle=\langle x_A+x_B,y_A+y_B\rangle \\ k\langle x_A,y_A\rangle=\langle kx_A,ky_A\rangle \end{gathered}[/tex]Use the second rule to find -2g:
[tex]\begin{gathered} g=\langle-2,1\rangle \\ \Rightarrow-2g=-2\langle-2,1\rangle \\ =\langle-2(-2),1(-2)\rangle \\ =\langle4,-2\rangle \end{gathered}[/tex]Find f-2g as f+(-2g) using the first rule:
[tex]\begin{gathered} f=\langle4,-3\rangle \\ \\ \Rightarrow f-2g=\langle4,-3\rangle-2\langle-2,1\rangle \\ =\langle4,-3\rangle+\langle4,-2\rangle \\ =\langle4,-3\rangle+\langle4,-2\rangle \\ =\langle4+4,-3-2\rangle \\ =\langle8,-5\rangle \end{gathered}[/tex]Therefore, the correct choice is:
[tex]\langle8,-5\rangle[/tex]