This is what I have done.

$\displaystyle (-4x+i)+(2-3yi)=6-2i$

Group real numbers and imaginary numbers

$\displaystyle (-4x+2)+(i-3yi)=6-2i$

$\displaystyle \Rightarrow$ Solve for real number

$\displaystyle -4x+2=6$

$\displaystyle -4x=4$

$\displaystyle x=-1$

$\displaystyle \Rightarrow$ Solve for imaginary number

$\displaystyle i-3yi=-2i$

$\displaystyle 3yi=3i$

.. Can someone verify if it's legal to divide both sides by $\displaystyle 3i$?