All possible answers for word-order when replacing pronouns in "Kannst du den neuen Kollegen den Besprechungsraum zeigen?" in English meaning "Can you show the briefing room to the new colleagues?" :
Kannst du ihnen den Besprechungsraum zeigen?
Kannst du ihn den neuen Kollegen zeigen?
Kannst du ihn ihnen zeigen?
On why all theses possibilities are right and using "ihm" is wrong:
"ihm" is the third person singular dativ pronoun meaning "to/for him" in English, while "den Besprechungsraum" in the main sentence is an akkusativ noun and can only be replaced by a personal akkusativ pronoun which is "ihn" for third person singular maskulin.
- Kannst du ihn den neuen Kollegen zeigen?
Although "den Besprechungsraum" is maskulin for "der Besprechungsraum" in nominativ, here we are showing the room to the people, not the other way around! (showing people to the room [as if room is a person!])
The only word order alteration in the sentence is for Nummer 2. and 3. where akkusativ pronoun comes first.
Kannst du ihn den neuen Kollegen zeigen?
Kannst du ihn ihnen zeigen?
Only Nummer 1. keeps the main sentence word order when using the dativ personal pronoun; from "den neuen Kollegen" to "ihnen" dativ third person plural.
- Kannst du ihnen den Besprechungsraum zeigen?
USEFUL UPDATE
As also answered on this topic (I completely quote the answer):
The object "den Kollegen" is dative plural. Hence, the other object "den Besprechungsraum"/"ihn" must be accusative. You can see it better in singular:
Kannst du dem Kollegen den Besprechungsraum zeigen?
Kannst du ihm den Besprechungsraum zeigen?
Kannst du ihn dem Kollegen zeigen?
Kannst du ihn ihm zeigen? (added to the quote)
As you can see, if there's a pronoun it always comes first, independant of the case.