John Gill Commentary Numbers 31:23

"everything that may abide the fire, ye shall make to go through the fire, and it shall be clean; nevertheless it shall be purified with the water for impurity: and all that abideth not the fire ye shall make to go through the water." — Numbers 31:23 (ASV)

Every thing that may abide the fire, you shall make it go through the fire Either through the smoke of the fire, and so be purified by suffumigation; or be put into the fire itself, where though they might be melted as the above things, yet not consumed as raiment, and vessels of skins, goats' hair, and wood, would be:

and it shall be clean accounted so:

nevertheless, it shall be purified with the water of separation with the water mixed with the ashes of the red heifer burnt, and sprinkled on it; see (Numbers 19:9)

and all that abideth not the fire without being consumed, as whatsoever is of wood

you shall make go through the water dip them in it, and rinse them there with a quantity sufficient; which the Targum of Jonathan says is forty seahs of water.