Wash your hands, you sinners, and purify your hearts, you double-minded.There are two statements here. The first has three key words: wash, hands, and sinners. The second has similar key words: purify, hearts, and double-minded.
If we look at the first three key words we see that the sinner, one who is practicing sin or given over to the occupation of sin, should wash or cleanse, that is remove the stains or make clean, the hands, that which the person is doing.
If we look at the second three key words we see that the double-minded, one who is wavering, uncertain, or divided in interest, should purify, that is set apart or clean, the heart, that is, the inner man.
So, outside and inside there is a call to be clean. Don't forget though that this directive comes immediately after the empowering words of the true powerlessness of Satan and the great desire of God to draw near to you.