I believe that "tycker" is the verb and "om" is a preposition. Together, they form a verbal phrase that translates to "like," but "om" still isn't a verb itself. (An example in English would be "put off," a combination of a verb and a preposition that together means "delay.")
So, "inte" comes after the verb "tycker" but before the preposition "om."
You're right in principle, however Swedish grammarians describe om (which by the way must always be stressed in this usage) as either a verb particle or an adverbial, so it's not a preposition. tycka om is a particle verb, but the negation may get between the verb and the particle.
im confused on this one, when you click the light bulb on the lesson and it gives you a description of the lesson it says at the bottom special cases, Swedish does not like to have two vowels next to each other, so if a word ends in a vowel, we drop the -e- in the ending. So why are there 2 e's in teet, wouldn't it just be tet