We always accept both de and dom, but we use de as the default. But it should really be the other way around - since there is a bug with "type what you hear" exercises, which causes only de but not dom to be accepted.
Do you happen to remember what the sentence was, so I can check it?
This isn't quite right. Let's explain it this way instead:
den and det both mean 'it', depending on gender. If you talk about 'the book', boken, you say den, but if you talk about 'the house' huset, you say det.
dem is the object form of the pronoun de which means 'they', so dem means 'them'
De tycker om det = They like it
De tycker om dem = They like them
You can hear the difference clearly in the spoken language because dem is pronounced as if it were written dom.
det is normally pronounced as if it were written de
It's just that they're talking about some object (concrete or abstract) that was previously mentioned, and since we don't know that context, we don't know what gender that object is, so both are accepted. The speaker knew what gender the object was though, so for them there was no choice.