Contradiction with Exodus 25:14
While 2 Samuel 6:4 describes the ark being transported on a cart, Exodus 25:14 instructs that the ark should be carried with poles on the shoulders of the Levites.
Exodus 25:14: And thou shalt put the staves into the rings by the sides of the ark, that the ark may be borne with them.
Contradiction with Numbers 4:15
2 Samuel 6:4 depicts the ark being transported by cart, whereas Numbers 4:15 warns against touching the holy things, including the ark, under penalty of death, which implies improper methods of transport like using a cart put those handling it at grave risk.
Numbers 4:15: And when Aaron and his sons have made an end of covering the sanctuary, and all the vessels of the sanctuary, as the camp is to set forward; after that, the sons of Kohath shall come to bear [it]: but they shall not touch [any] holy thing, lest they die. These [things are] the burden of the sons of Kohath in the tabernacle of the congregation.
Contradiction with Deuteronomy 10:8
2 Samuel 6:4 shows an ox cart carrying the ark, but Deuteronomy 10:8 specifies that the Levites are set apart to carry the ark, not using any animal or cart.
Deuteronomy 10:8: At that time the LORD separated the tribe of Levi, to bear the ark of the covenant of the LORD, to stand before the LORD to minister unto him, and to bless in his name, unto this day.