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

cos(a) = cos(b) if and only if a = 2nπ ± b
where n is an integer.

So, we have:

3x - π/6 = x + π/4

Subtract x from both sides:

2x - π/6 = π/4

Add π/6 to both sides:

2x = π/4 + π/6
2x = 3π/12 + 2π/12
2x = 5π/12

Divide by 2:

x = 5π/24

Therefore, the solution to the equation is x = 5π/24.