As + adjective + as
Used to make comparisons when things we are comparing are equal in some way.

“My hair is as long as yours”
“You need to do it as carefully as you can”
“My cousin is as tall as you”

Not as + adjective + as
Used to make comparisons between things that are not equal.

“It’s not as heavy as I thought it would be”
“My hair is not as long as yours”
“She’s not singing as loudly as she can”