"Mohamed's restaurant is expensive but good."
Translation:مَطْعَم مُحَمَّد غالي لٰكِنّ طَيِّب.
in Genitive relations between two words, the definite article is added to the second word, in the same way almost where you put ('s) in English. Examples:
the cop's car: سيارة الشرطي
the man's hat: قبعة الرجل
the woman's dress: ثوب المرأة
and so on. Here though, because "Mohammed" is a proper name, it is then defined on its own and we can't add "al" to it, of course. Hence, مطعم محمد .
The grammatical construction covered in this exercise ("Mohamed's restaurant") is called the idafah (lit. addition) - the English equivalent is simply the genitive construction. Now regarding your question, the first term of the idafah is never preceeded by the definite article. The definiteness of the second term is sufficient to make the whole idafah definite. The examples, mentioned in TJ's answer, are perfect in order to understand what I am talking about.