2 Timothy 3:10

Here the apostle, to confirm Timothy in that way wherein he walked, I. Sets before him his own example, which Timothy had been an eye-witness of, having long attended Paul (Ti2 3:10): Thou hast fully known my doctrine. The more fully we know the doctrine of Christ and the apostles, the more closely we shall cleave to it; the reason why many sit loose to it is because they do not fully know it. Christ's apostles had no enemies but those who did not know them, or not know them fully; those who knew them best loved and honoured them the most. Now what is it that Timothy had so fully known in Paul? 1. The doctrine that he preached. Paul kept back nothing from his hearers, but declared to them the whole counsel of God (Act 20:27), so that if it were not their own fault they might fully know it. Timothy had a great advantage in being trained up under such a tutor, and being apprised of the doctrine he preached. 2. He had fully known his conversation: Thou hast fully know my doctrine, and manner of life; his manner of life was of a piece with his doctrine, and did not contradict it. He did not pull down by his living what he built up by his preaching.

— Matthew Henry's Concise Commentary (public domain)

fully known--literally, "fully followed up" and traced; namely, with a view to following me as thy pattern, so far as I follow Christ; the same Greek as in Luk 1:3, "having had perfect understanding of all things." His pious mother Eunice and grandmother Lois would recommend him to study fully Paul's Christian course as a pattern. He had not been yet the companion of Paul at the time of the apostle's persecutions in Antioch, Iconium, and Lystra (Act 13:50; Act 14:5, Act 14:19), but is first mentioned as such Act 16:1-3. However, he was "a disciple" already, when introduced to us in Act 16:1-3; and as Paul calls him "my own son in the faith," he must have been converted by the apostle previously; perhaps in the visit to those parts three years before. Hence arose Timothy's knowledge of Paul's persecutions, which were the common talk of the churches in those regions about the time of his conversion. The incidental allusion to them here forms an undesigned coincidence between the history and the Epistle, indicating genuineness [PALEY, HorÃ&brvbr PaulinÃ&brvbr]. A forger of Epistles from the Acts would never allude to Timothy's knowledge of persecutions, when that knowledge is not expressly mentioned in the history, but is only arrived at by indirect inference; also the omission of Derbe here, in the Epistle, is in minute accordance with the fact that in Derbe no persecution is mentioned in the history, though Derbe and Lystra are commonly mentioned together.

— Jamieson-Fausset-Brown Commentary (public domain)