12x-12y it's distributive property i don't get it

Distributive Property basically means that you have an expression, and every value in that expression is multiplied or divided by the same thing. 
So for your example, you divide everything by 12. But since it is an expression, not an equation, you can't get rid of the 12 and be done. You have to put it somewhere so that it remains in the equation. Thus, 12(x-y)

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.