The word "defilements" refers to sinful behavior that makes one morally impure. The "world" refers to human society. AT: "the defiling practices of sinful human society" (See: rc://en/ta/man/translate/figs-metonymy)
You can translate "knowledge" using a verbal phrase. See how you translated similar phrases in 2 Peter 1:2. AT: "by knowing the Lord and Savior Jesus Christ" (See: rc://en/ta/man/translate/figs-abstractnouns)
"their condition is worse than it was before"
Peter speaks of life as a "way" or path. This phrase refers to living a life that is according to God's will. (See: rc://en/ta/man/translate/figs-metaphor)
"Turn away" here is an idiom for "change direction from." AT: "change direction from following the holy commandment" (See: rc://en/ta/man/translate/figs-idiom).
This can be stated in active terms. AT: "the holy commandment that God brought to them" (See: rc://en/ta/man/translate/figs-activepassive)
"Delivered" here is a metaphor for "brought." (See: rc://en/ta/man/translate/figs-metaphor).
"This proverb applies to them" or "This proverb describes them"
Peter uses two proverbs to illustrate how the false teachers, although they have known "the way of righteousness," have turned back to the things that make them morally and spiritually impure. (See: rc://en/ta/man/translate/writing-proverbs)