It doesn't matter how long Jesus lived when it comes to his active obedience. He did everything necessary according to the Law - including being the sacrifice for sins. What matters is that he is God in flesh (John 1:1,14; Col. 2:9), and because of his divine nature (Jesus is both divine and human, see the Two Natures of Christ) his obedience is perfect and of infinite value. Therefore, he is able to impute to us, by faith (Rom. 5:1), his righteousness so that we have a righteousness that is not our own (Phil. 3:9).
Jesus' active obedience is the teaching that he fulfilled the Law. He was born under the Law (Gal. 4:4) and fulfilled the Law perfectly because he never sinned; that is, he never broke the Law (1 Peter 2:22). It is called active obedience because it is something that Christ did in an active sense, by walking, talking, fulfilling the legal requirements of Old Testament law. This is in contrast to the passive obedience which states that Christ allowed himself to be led to the cross to be crucified and thereby atone for our sins.