16:2a When David had finished sacrificing the burnt offerings and peace offerings,

David completed ⌊giving⌋ the burnt offerings and the peace offerings.
-or-
David finished sacrificing the offerings ⌊that were to be⌋ burnt ⌊completely⌋ . ⌊He also finished sacrificing⌋ the offerings ⌊for keeping their⌋ relationship ⌊with God⌋ .

16:2b he blessed the people in the name of the LORD.

⌊When he did that,⌋ he blessed the people with the authority of Yahweh.
-or-

⌊After he finished doing that,⌋ he asked Yahweh to bless the people ⌊by doing good to them⌋ .

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