If your wood is very thick, and the posts will not reach, there are two solutions. The traditional solution is to counterbore in order to reach the post. This drawing shows a counterbored post. Period posts or cotter pins were often too short; and early cabinetmakers were forced to chisel in order to reduce the thickness of the wood where the post passes through. Today's cabinetmaker might prefer a spade or Forstner bit.
The second solution is to use post extenders. These are internally threaded bolts which spin on the post from the inside of the drawer.

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Horton Brasses Inc., 49 Nooks Hill Road, Cromwell CT 06416, 800-754-9127