Gave a complete report of everything (literally “told them one by one each of the things”) is translated “gave a detailed account” by Jerusalem Bible (see also Phillips and New English Bible).

Work (most translations “ministry”) is the same word used in 1.17.

As in a number of instances, it is sometimes difficult to translate an expression which speaks of the person doing something through someone else; therefore the last clause of verse 19 may be rendered as “what God had done among the Gentiles because of the work which Paul did.” Sometimes the relationship between the accomplishing and the working is expressed in two closely combined clauses without formal connection—for example, “everything that God had accomplished among the Gentiles; Paul had done the work.”

Quoted with permission from Newman, Barclay M. and Nida, Eugene A. A Handbook on The Acts of the Apostles. (UBS Handbook Series). New York: UBS, 1972. For this and other handbooks for translators see here .