I live in California and I'd like to know when I'm hired thru an agency for only a 6 months of contract work and after my contract is done, can I apply for unemployment and will I be accepted?
I can't answer that. You should understand that if you go to work through a "temp agency" you become the employee of the temp agency.
If they do not have another job for you it would be a lack of work claim, but temp agencies do not just tend to lie down and pay unemployment due to "lack of work claims" they offer additional assignments, but not all those assignment they offer may be "suitable" to you .. so you refuse the assignment.
This sets up the possibility for a protest to your claim if you refuse a new assignment. Some states, although not California, actually have special provision for which have additional requirements to meet.