In short
Jairus specifically asked for the laying of hands because, as the synagogue ruler, he had probably already seen Jesus heal in that way (see Matthew 8:3, Matthew 8:14). Jesus’ word had power to heal the sick, and he exercised this power in the laying on of hands (see Exodus 29:10, Matthew 9:21, Acts 8:16–25).
Jairus specifically requested for the laying of hands because, as ruler of the synagogue, he most likely had already witnessed Jesus conduct several miraculous healings in this way (see Matthew 8:3). The words that Jesus spoke were powerful enough to heal the sick, and this power was transferred by means of the laying of hands (see Exodus 29:10, Matthew 9:21, Acts 8:16–25).1
18 While he was saying these things to them, behold, a ruler came in and knelt before him, saying, “My daughter has just died, but come and lay your hand on her, and she will live.”