I am a 42 yr old female I weigh 125 pounds. I drank 4 beers before 9pm. Will alcohol be detectable in my urine 12 hours later?

That will depend on the type of test. If it tests only for the presence of alcohol (EtOH) you should be clear. If however it is screened for ethylglucuronide (EtG) the fact that you have consumed alcohol in the recent past well be detectable by the presence of this metabolite.