As with all verbs that have an object the place of that object is after verb, at least in those cases when the object is represented by a noun phrase in which the head is a noun: subject - verb (conjugated) - object. (When the noun head is a pronoun the object is placed before the verb.¹)
In your sentence, the verb "préférer" appears as a past participle, not a conjugated verb and so here is below first what corresponds to your question; the correct way to phrase this idea about preference by means of the verb "préférer" is as follows.
- Elle préfère la cuisine libanaise et la cuisine italienne.
- Elle préfère la cuisine libanaise et l'italienne. (alternative, explained below (Grevisse))
- Elle préfère les cuisines libanaise et italienne. (other alternative)
Instead, of the conjugated verb you can have a construction with the past participle of the verb and you use it then as an adjective. That's done in the sentence you write but there are big errors as the pronoun "elle" can't be used in it and an "adjectif possessif" (ses) must be used; on top of that, as you are talking about two types of cooking a verb in the plural is necessary.
- Ses cuisines préférées sont la cuisine libanaise et la cuisine italienne.
Ses cuisines préférées sont la cuisine libanaise et l'italienne. (alternative)
(Grevisse) A noun used with an adjective can be omitted if it has been already mentioned. The adjective without noun is preceded by the determiner that the noun would have had. This turn is mostly found in the written language.
Sa cuisine préférée est la cuisine italienne.
Every time you can use a verb there is an equivalent way making use of the corresponding noun.
- Elle préfère la cuisine italienne.
- Elle a une préférence pour la cuisine italienne.
¹ addition prompted by user aCOSwt