Yeah.. Fixed my bad

Explanation

Using the Bowtie method, you find that $\frac{x+y}{xy}$=6.

By multiplying both sides of the second equation by $\frac{-1}{2}$, you find that $\frac{1}{6}=\frac{zy}{z+y}$.

Flipping both fractions yields $\frac{z+y}{zy}=6$, and thus, $\frac{z+y}{zy}=\frac{x+y}{xy}$.

Inspecting the two fractions, you may realize that z must equal x.

Alternatively, by applying the Bowtie again, you obtain $\frac{y + x}{zy} = \frac{z + y}{xy}$, and thus $zy^2 + xyz = xyz + xy^2$, meaning $zy^2 = xy^2$, or z = x, so the answer is choice (C).

answer: C
1/x + 1/y = 6
(x + y) / xy = 6

-1/3 = -2 (zy/(z + y))
(z + y) / zy = 6

(x + y) / xy = (z + y) / zy
(x + y) / x = (z + y) / z
1 + y/x = 1 + y/z
y/x = y/z
1/x = 1/z
x = z

Answer is C

Expand the 1st given Equation and you get 6 = x+y / xy

Expand the 2nd Eqn and you will get 1/6 = zy/y+z

Substitute the value of 6 from 1st Equation and you get the answer after cancelling the common terms both sides.