Confused with these distributive property problems. i am asked to verify the distributive property in them but i dont get why one number is used twice for example;
6 × (2 + 10)
6 × 2 + 6 × 10 < --here in this part why is the 6 used twice after applying the distributive property? and why do you have to multiply by it afterwards?

The 6 out front tells you to multiply 6 to the sum in the parenthesis, in this case being 12, so 6*12=72.
If you use the distributive property you are not going to add the 2 and 10 first but instead multiply the 6 to each of them separately and add last. So, 6*2 + 6*10= 12+60 = 72
You get the same answer just doing it a different way.