What's happening here grammatically when "phone number" is translated as "رَقَم هاتِف" (lit. "number phone")?
The word order in Arabic is normally like that, e.g. literally 'a cat black' or 'the house of Omar'. So same here: The number of the phone.
Oh, it's an iDaafa construction! That makes sense!
Which means that "رَقَم هاتِف اَلْمُهَنْدِس" for "the engineer's phone number" must be a nested iDaafa construction.