What is x if x-6i/x-i = 3+yi?

Answer 1

Are you talking about (x-6i)/(x-i) = 3+yi ?
Please put parenthesis there, otherwise people would be confused.
Since (x-6i)/(x-i) = 3+yi
we have: x - 6i = (x-i)(3+yi) = (3x + y) + (xy - 3)i
therefore the real parts must be the same at both sides of the equation, and the imaginary parts must be the same at both sides of the equation, too:
x = 3x + y.......................(1)
6 = 3 - xy........................(2)
From (1): y = -2x
put in (2): -3 = xy = x*(-2x)
Therefore: x^2 = 3/2
or: x = +-sqrt(3/2)

Answer 2

I have absolutely not a clue. Maybe you could try doing homeowrk on your own, though.