First, I’ve only seen this syntax referred to as “TK constructions” in one place and it seems that it’s not really referred to that way elsewhere.
What’s so interesting about this construction?
It’s this: in English we can say “We were talking about what you wanted.” But in Russian, you can’t glue the phrases together that readily. “what” must be in the prepositional case (о том ) for the sake of the first clause, but it also has to function as a direct object of хотела . Since it can’t exist in two cases at one, we have to glue it together somehow. That’s what this construction does.
The way we do that is like this: Мы говорили о том, что ты хотела.
Many prepositions will require this type of construction. For example:
Наше решение зависит от того, что он хочет. (“Our decision depends on what he wants.”)
These constructions can get quite complicated with two prepositions in two different clauses referring to the same thing appearing in two different cases. For example:
Мы думали о том, на чём вы вчера настаивали. (“We were thinking about what you were insisting on yesterday.”)