Here's why this is a problem:
* Pronoun Agreement: Pronouns should agree in number (singular or plural) with the noun or pronoun they refer to (the antecedent).
* Singular vs. Plural: "Everyone" is singular because it refers to every individual person in a group. "Their" is plural because it refers to multiple people.
To correct the sentence, you have a couple of options:
1. Use a singular pronoun:
* "Everyone needs to take his or her project home by Friday." (This can sound awkward if repeated often)
* "Everyone needs to take their project home by Friday." (While technically incorrect, this is increasingly accepted in informal writing, but avoid it in formal contexts)
2. Reword the sentence to avoid the pronoun:
* "All students need to take their project home by Friday."
* "Each person needs to take their project home by Friday."
The best choice depends on the context and style of your writing.