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Use a hammer to flatten out the head and tip of a small nail (Image 1). This will turn the nail into a small blade.
Working from the outside of the drawer, drill a hole in the place you want the countersunk hole (Image 2).
Insert the tip of the flattened nail through the inside of the drawer, and attach the pointed tip of the nail to the drill.
Turn on the drill. Instead of pushing and drilling, pull upward and drill. A few revolutions will produce a perfect countersunk hole.