My translation of “seeking” was rejected, but “looking for” and “seeking” are interchangeable
i feel it should be ：what are you looking for in THIS apartment? otherwise, it will be "co hledáte v tamtom bytě"
For an emphatic "that" you can use tamten/tamta/tato or tamhleten/tamhlleta/tamhleto.
For "this" you can use tenhle/tahle/tohle or (more formally, in writing) tento/tato/toto.
However, in this course ten/ta/to is never "this". It is less definite than tamten or tamhleten, etc, but it is translated as "that" or often as "the".