Wipe the dust or debris off the surface of the wall with a clean microfiber cloth.
Fill a clean bucket with 1 gallon of lukewarm water. Add 1/4 to 1/2 cup of gentle dish soap to the water and stir with a wooden spoon for several seconds.
Submerge a microfiber cloth in the solution and wring out the excess soapy mixture. Start at the top of the Honduran mahogany wall and wipe the wood clean with the damp cloth. Work in small sections while moving down the wall.
Remove the soapy solution from the wood with a microfiber cloth dampened only with water. Dry the Honduran mahogany wall with a clean microfiber cloth.
Create a homemade furniture polish for the mahogany wood by mixing equal parts water and white vinegar. Rub the mixture into the wood with a soft cloth dampened in the polish. Buff the wall dry with a chamois cloth.