To solve this equation, we can use the trigonometric identity:

sin(A-B) - sin(A+B) = 2cosBsinA

Given:

A = π/6
B = x

Therefore, the equation becomes:

2cos(x)sin(π/6) = √2

Using the values of sin(π/6) = 1/2 and cos(π/6) = √3/2, the equation simplifies to:

2(√3/2)sin(x) = √2
√3sin(x) = √2
sin(x) = √2/√3
sin(x) = √6/3

Therefore, the solution to the equation sin(π/6-x)-sin(π/6+x) = √2 is sin(x) = √6/3.