Since there are 1000 milliliters in 1 liter, then 3 liters is equal to 3 x 1000 = <<3*1000=3000>>3000 milliliters.
She needs to drink 3000/500 = <<3000/500=6>>6 sets of 500 milliliters of water.
So, she will be able to drink a total of 3 liters after 6 sets x every 2 hours = 12 hours.
#### 12