Remember the definition of the commutation relation

`[a,b]=ab-ba`

Preform this operation on `[S_x*S_y,S_y]`

`[[S_x*S_y,S_y],S_z]=[[S_x*S_y*S_y-S_y*S_x*S_y,S_z]`

The following is the commutation relation for spin 1/2 systems.

`[S_x,S_y]=i barh S_z`

For cyclic permutations of `x` , `y` , and `z` . `barh ` is represents the reduced planks constant here.

`=[[S_x,S_y]S_y,S_z]`

`=[i barh S_z*S_y,S_z]`

`=i barh S_z[S_y,S_z]`

`=-barh^2S_z*S_x`