4(x-2)=4x-8 is this equation always true

Yes, 4(x-2) is 4 times x-2 which using the distributive property gives you 4x-8 because 4 times x is 4x and 4 times -2 is -8 so you would always get 4x-8

Distribute 4 over the parentheses:-

4(x - 2) = 4x - 8  which is identical to the right side.

Yes  - this is always true for any values of x,  and its called an identity.