The properly formatted example is the last one:
Romans were very particular in their dining habits. They reclined on "special couches" (Phin 429).
For an in-text citation in Modern Language Association (MLA) style, you give a parenthetical reference to your source by an author name and page number. The full information about that author and source will be included in your bibliography.
So in the examples shown, the third example is incorrect because it only lists a page number, not the author name.
The second example shown is incorrect because it splits apart the reference to the author (Phin) from the reference to the page number (429).
The first example is close to correct, but is punctuated incorrectly. The in-text citation in MLA style is considered part of the sentence, so the period goes at the very end of the whole sentence, which means after the reference (Phin 429).
Thus the fourth example shown is the only one that is fully correct in its format.
