Solve sin ( 6 x ) cos ( 8 x ) − cos ( 6 x ) sin ( 8 x ) = − 0.85 for the smallest positive solution.

Note that  :

sin (8x - 6x)   = sin 8x cos 6x  -  cos 8x sin 6x     ....so......

-sin (8x - 6x) =  cos 8x  sin 6x  - sin 8x cos 6x   ...... and this implies that.......

-sin (8x - 6x)  = -0.85

sin (2x)  = 0.85

Using the sine inverse 

arcsin (0.85)   = x =  about 58.21°

So.....dividing this angle  by 2,   x = about  29.105°

Here's a graph of the solution :  https://www.desmos.com/calculator/u95uehqy1i