"صَحيفة اَلْمُهَنْدِس بُنِّيّة."
Translation:The engineer's newspaper is brown.
She says "saHiifatil muhandis" because she streams the reading and makes all endings are in sukuun. The "T-sound" comes from ة ta marbuTa, which is not pronounced if we stop the word. When we stop the reading at ة, it becomes ه (h).
Nb: if we follow Formal Standard, the pronunciation for the phrase above is "saHiifatul muhandisi" (with the -tu sound) as it is (the subject) in the nominative case.
"The engineer's brown newspaper" would be:
صحيفةُ المهندسِ البُنِّيّةُ
SaHiifa(tu) 2al-muhandis(i) 2al-bunniya(tu).
Applying Formal Standard (ie. with ending sounds) will make the case clearer. The ending sound of البُنِّيّةُ follows صحيفةُ as البُنِّيّةُ is the attributive adjective of صحيفةُ, which becomes definite by المهندسِ in the structure of 2iDaafa الإضافة.