Option 1 -> "Resolve" is the base verb or noun meaning determination, but "New Year's resolve" is not the standard phrase.
Option 2 -> "Resolving" is the gerund form, but "New Year's resolving" is grammatically incorrect in this context.
Option 3 -> "Resolvation" is not a valid word in English.
Option 4 -> "Resolution" is the correct noun form used in the common phrase "New Year's resolution."
Hence, Option 4: resolution -> "New Year's resolution" is a standard idiomatic expression referring to a promise or goal that people commit to at the start of the year, and "resolution" is the proper noun form derived from "resolve" -> correct