"You can terminate the contract after 12 months..."

Is,

“You can terminate the contract after 12 months by giving 2 months notice.”,

equivalent to,

“After 12 months, by giving 2 months notice, you can terminate the contract.”?

Does the second statement make sense? Obviously a contract isn’t terminated by giving 2 months notice, its terminated by giving 2 months notice and then continuing it for 2 more months. You can’t terminate something by giving notice that in 2 months you will terminate it, assuming it can only be terminated once, so the second statement does not make sense.

Do the statements have the same meaning? Does either make sense?

Yes, the statements have the same meaning, the second sentence uses a non-restrictive appositive noun phrase; en.wikipedia.org/wiki/Apposition .