How many priests carried the ark of God across river Jordan?
In the building of the ark we find:
"You shall cast four rings of gold for it, and put them in its four corners; two rings shall be on one side, and two rings on the other side. And you shall make poles of acacia wood, and overlay them with gold. You shall put the poles into the rings on the sides of the ark, that the ark may be carried by them. The poles shall be in the rings of the ark; they shall not be taken from it" (Exodus 25:12-15).
The ark was carried by the sons of Kothah, one of the three sons of Levi.
"And when Aaron and his sons have finished covering the sanctuary and all the furnishings of the sanctuary, when the camp is set to go, then the sons of Kohath shall come to carry them; but they shall not touch any holy thing, lest they die. These are the things in the tabernacle of meeting which the sons of Kohath are to carry" (Numbers 4:15).
"So Moses wrote this law and delivered it to the priests, the sons of Levi, who bore the ark of the covenant of the LORD, and to all the elders of Israel" (Deuteronomy 31:9).
"Then David said, "No one may carry the ark of God but the Levites, for the LORD has chosen them to carry the ark of God and to minister before Him forever"" (I Chronicles 15:2).
When the ark was carried into Canaan, the ark was carried by the Levites, accompanied by the priests. "So it was, after three days, that the officers went through the camp; and they commanded the people, saying, "When you see the ark of the covenant of the LORD your God, and the priests, the Levites, bearing it, then you shall set out from your place and go after it" (Joshua 3:2-3). Yet, later the text just talks about the priests who bore the ark: "Then the priests who bore the ark of the covenant of the LORD stood firm on dry ground in the midst of the Jordan; and all Israel crossed over on dry ground, until all the people had crossed completely over the Jordan" (Joshua 3:17). This may mean that the Levites who carried the furnishings of the Tabernacle were numbered among the priests, even if they were not directly descendents of Aaron. Or it may be the fact that since the priests all descend from Aaron and Aaron was a descendent of Kothah that both priests and non-priests who were descendents of Kothah carried the ark. In the case of the crossing the Jordan, all who were carrying the ark were priests. You can also see this in "So all the elders of Israel came, and the priests took up the ark. Then they brought up the ark of the LORD, the tabernacle of meeting, and all the holy furnishings that were in the tabernacle. The priests and the Levites brought them up" (I Kings 8:3-4).
Most people assume that four men carried the ark. That could be, but I found verses like:
"Therefore Zadok and Abiathar carried the ark of God back to Jerusalem. And they remained there" (II Samuel 15:29 -- but note that each had a son with him (II Samuel 15:27)).
"And David called for Zadok and Abiathar the priests, and for the Levites: for Uriel, Asaiah, Joel, Shemaiah, Eliel, and Amminadab. He said to them, "You are the heads of the fathers' houses of the Levites; sanctify yourselves, you and your brethren, that you may bring up the ark of the LORD God of Israel to the place I have prepared for it. For because you did not do it the first time, the LORD our God broke out against us, because we did not consult Him about the proper order." So the priests and the Levites sanctified themselves to bring up the ark of the LORD God of Israel. And the children of the Levites bore the ark of God on their shoulders, by its poles, as Moses had commanded according to the word of the LORD" (I Chronicles 15:11-15).
Here six Levites are named. It is possible that they rotated the duty between them in some manner or they could have all carried it together. We aren't told how long the poles were or the details of how the ark was carried.
There is no way to tell for certain how many men carried the ark or even if the same number of men were used every time.