He secretly started to pull a gun out of his business suit.
You know 抜く from before, it's to extract. Then you have 出す which is to remove. So, if you extract and remove something, you are moving to extract something. By extracting it you are also going to select it as well.
The readings are from 抜く and 出す, combined together. Know those two and you'll be able to read this word as well.