Multiple choice answers:

3
1/3
-1/3
-3

If you have a calculator it would be easy yoo plug in y= so I’ll just help it’s C

This is tricky
lets try  substituting  y = √)6x - 9)

√(6 - y) + √(6x + y) = √6

squaring both sides:-

6 - y + 6 + y - 2√(6 - y)(6 + y) = 6
12 - 2√(6 - y)(6 + y) = 6
√(6 - y)(6 + y) = (6-12) / -2 = 3
Squaring both sides:-
(6 - y)(6 + y) = 9
36 - y^2 = 9
y^2 = 27
y = +/-√27

√(6x - 9) = +/- 27

6x - 9 = 729

x = 738/6  =  123

This cannot be a solution because   we would have a negative value for the 
second square root

I would say that no solution exist.