you need figure out the old dimensions. Take out the old one and install the new 8" pipe male end down, in to the collar and snap it shut.Slip the 12" pipe male end up and continue this process till the roof.
Insert 8" pipe: male end DOWN into the inner collar to snap shut. Slip 12" pipe:male end UP over the other pipe and collar. Continue this process till roof opening.
First thing we need to take out the old one dimension and replace with new one.The temco chimney may be tough, we usually can't line those or can tear out either one and replace them with a new ZC efficient EPA fireplace.
I would read the instruction manual, assuming one was given. I would then follow those instructions. If that failed or were it too complicated I would just call a professional to install it.