To Inspect
To Examine, To Check
する verb
You examine the problem. In order to do this, you need to inspect it or to examine it. And if you're inspecting people like this, you're probably the police.
けんもんする
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
警察が私の車を検問している時、どきどきしました。
While the police were inspecting my car, my heart was racing.