The front finish of your wood kitchen cabinets can become caked in tough grease, dirt, and grime over time from cooking in the kitchen. So, today I'm going to show you how to clean that tough gunk buildup off of your finished wood kitchen cabinets in just a few easy steps!To do this, you will need: First, pour a small amount of liquid dish soap in the kitchen sink and fill the sink with a few inches of warm tap water.Next, submerge a clean sponge in the warm sudsy water and then squeeze out any excess water in the sponge.o, today I'm going to show you how to clean that tough gunk buildup off of your finished wood kitchen cabinets in just a few easy steps! To do this, you will need: First, pour a small amount of liquid dish soap in the kitchen sink and fill the sink with a few inches of warm tap water.