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.

Sustainability. We choose our packing materials with the planet in mind. We use popcorn and newspaper. The popcorn, made from cornstarch, is a harmless alternative to Styrofoam. It is completely biodegradable and dissolves in water. The newspaper we use represents the ultimate recycling. Our employees bring it in and we reuse it!
Horton Brasses Inc., 49 Nooks Hill Road, Cromwell CT 06416, 800-754-9127