Needs cure for increasing cuts cracks and itching in both hand palm, aggravate with detegents use.

Dermatitis: This could be reaction to exposure to detergents. Could be an allergy or a fungus infection. Should avoid exposure by using gloves when using the detergents. Could try some cortisone cream and moisturizers. If not better then see the doctor for a diagnosis.

Hand eczema: Sounds like you have hand eczema. Treatment is to avoid hand irritants and solvents. Then to regularly apply topical mid to high potency steroids.