Here are a few ideas you might find helpful.
Dampen a clean, dry cloth with undiluted white vinegar, and wipe down greasy cabinets. Rinse your cloth with warm water, wring out most of the moisture, and use it to rinse the cabinetry. Dry the damp surfaces with a paper towel, but note any still-sticky spots that need a do-over.
Hi Mary: Here's one idea:
Supplies Needed To Degrease Your Kitchen Cabinets:
1/2 cup Borax
1 cup Distilled Vinegar
1 Gallon of Very Hot Water
In order to make this process work you are going to need roughly 1 gallon of hot water. Mix the amounts as listed above until completely dissolved. Then get started on cleaning your cabinets.
Here's a site with another idea:
TSP or Krud Kutter.
Here's a good video tutorial: https://www.youtube.com/watch?v=Rqq5k9LFkeE
Use a gentle degreaser. You can begin with a paste of baking soda & hydrogen peroxide but if that doesn't get it, go with something commercial. My choice would be Fuller or GP66. Make sure whatever you use is safe for wood and not abrasive.