Translation:We are carrying the table into the garden.
If it was 'dem,' it would imply that they were carrying it around in the garden. 'Den' means that they were bringing it into the garden from some other location. German uses 'in' to mean both 'in' and 'into,' so the only way to clarify the meaning is the case used for the direct object.
Generally you use accusative for the direct object and dative for the indirect object.
I agree with slendro. My "webster's New World German/English" dictionary has 'to carry" and "to take" as the first 2 definitions of tragen. Furthermore, if you look at an English thesaurus, "carry" and "take" are synonyms. Though I agree to carry is a more specific method of taking, but in daily usage, (at least for American English), to carry the table and to take the table to the garden would mean the same thing.