Radhika was given 12 video games on Christmas and 8 video games on her birthday, so she was given 12 + 8 = <<12+8=20>>20 video games.
She had 1/2 this many before she was given gifts, 20 / 2 = <<20/2=10>>10 video games she already owned.
She was given 20 video games and had 10 already, 20 + 10 = <<20+10=30>>30 video games.
Now Radhika has 30 video games.
#### 30