2 Samuel 23:8

8 These be the names of the mighty men whom David had: The Tachmonite that sat in the seat, chief among the captains; the same was Adino the Eznite: he lift up his spear against eight hundred, whom he slew at one time.

1 Chronicles 11:11

11 And this is the number of the mighty men whom David had; Jashobeam, an Hachmonite, the chief of the captains: he lifted up his spear against three hundred slain by him at one time.

The passage in 2 Samuel says David's chief captain slew 800 with a spear, at one time. The passage in 1 Chronicles says that his chief captain slew 300 with a spear, at one time.

One view is that these are different people. In 2 Samuel, the chief captain is named Adino, and in Chronicles the chief captain is called Jashobeam.

There are also contextual indications that these chapters are set at different time periods in David's reign:

2 Samuel 23:1

1 Now these be the last words of David. David the son of Jesse said, and the man who was raised up on high, the anointed of the God of Jacob, and the sweet psalmist of Israel, said,

1 Chronicles 11:9

9 So David waxed greater and greater: for the Lord of hosts was with him

The chapter in 2 Samuel is set towards the end of David's life, whereas the chapter in 1 Chronicles is during the time when David is rising in power. Between those two points, David's chief captain changed. David reigned for forty years (2 Samuel 5:4), meaning this probably happened a half dozen times or more as the captains aged out.

Another reconciliation is to point out that 300 is a subset of 800, and if someone slew 800 soldiers, it is also true that they slew 300 soldiers.