so it seems you have the object modeled. You may have it “outside” of the piece component. You may need to put it inside the component so that the hole edges can interact with the piece surface, and you can therefore erase the face in the oval and see inside.
You are most likely correct. Being a newbie, I just moved the component onto the object. I then tried to intersect the two, but probably do not yet understand how two objects interact.
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Your profile says you have Pro, so you should be able to use the Solid Tools to subtract the pocket hole from the board.
Give it a try. Since you downloaded it, no telling if it was done properly and if it will lie on the face correctly.
You will eventually make your own holes: just make the cylindrical shape that the drill makes, intersect faces with your piece and delete the parts that you don’t need. And you’ll pick up steps to make it easier. Even easier than opening the 3DWH
I just use intersect. but solid tools is OK. Then you skip the step of having to erase so much. But you add the skill it takes to make solid components–which is good to know.