Hi, I turned 24 in June 2019. I lived with my parents the whole year until October 2019 when I moved to Florida for a job. Can they claim me as a dependent?

Probably not, unless your total income for the year was less than $4200.

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit.

Since you are over 23, you cannot be a QC. So, now there is an income test. 

A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:

1. Closely Related OR live with the taxpayer ALL year  
2. His/her gross taxable income for the year must be less than $4200 ($4150 in 2018)
3. The taxpayer must have provided more than 1/2 his support

In either case:

4. He must be a US citizen or resident of the US, Canada or Mexico
5. He must not file a joint return with his spouse or be claiming a dependent of his own
6. He must not be the qualifying child of another taxpayer