Remove the cabinet door from the cabinet and take off the kickplate by unscrewing it or prying it off.
Scrape away any adhesive on the cabinet door, using a metal putty knife or other scraper that's safe for the cabinet material.
Use a solvent made with citric acid for a low-odor, water-soluble mix. Apply the product liberally to the remaining adhesive. Solvents come in a spray bottle or can be applied by soaking a rag and applying it by hand.
Let the solvent work for at least 15 minutes. Some work so well that you may only have to rinse and wipe it off when it's done. If adhesive remains on the cabinet, continue to the next step.
Scrub off the adhesive with fine steel wool and additional solvent. Since another kick plate will likely be installed, scratches should be of no serious consequence.