Mark 6:7-13 narrates how Jesus sends out his chosen Twelve to be his extensions in the proclamation of the kingdom. The Twelve are mentioned first in Mark 3:14-19. The verses in Mark 3:14-15 are to be noted and their correspondences with the present section:
Twelve men were chosen to represent the Twelve tribes of Israel which Jesus is reconstituting with his work. The Twelve are also called "apostles", a word drived from the verb apostellw , "I send". They are therefore the "sent ones." When the Twelve are sent out, their period of being-with Jesus has ended; they can now extend his presence as they do the very things he has been doing: to preach repentance and to bring about healing. (Note however that Mark 6:13 mentions the anointing with oil, something that we don't see Jesus doing. The fact that in James 5:14 it has become a standard practise for the sick makes one think that perhaps Mark is reporting something that the apostles developed on their own with the implicit approval of Jesus.
The apostles are sent out two-by-two since it is safer to travel with a companion. There are therefore six pairs of apostles, perhaps corresponding to the six days of creation as they labor towards the Sabbath rest, "the day without sunset" as St. Augustine would call it. (The idea is suggested more by the Preface for the Apostles than by exegesis: "Qui gregem tuum, Pastor aeterne, non deseris, sed per beatos Apostolos continua protectione custodis, ut iisdem rectoribus gubernetur, quos Filii tui vicarios eidem contulisti praeesse pastores.")
The list of the apostles in 3:16-19 may reflect -- at one time or another -- how they were paired. Compared to the lists in Matthew 10:2f and Luke 6:12f the list in Mark differs in that Simon Peter is paired with James, the brother of John while Andrew is paired with John, the other half of the Boanerges. .In Luke and Matthew, the brothers are paired with one another. Again, while Matthew and Mark concur in their pairings of the last four apostles, in Luke we find James of Alphaeus going with Simon the Zealot and Thaddeus going with Judas the Iscariot. However, from these lists alone one cannot make a definite judgment on who went with whom.
To be noted in these lists is the pre-eminence given to Simon Peter who is always mentioned first. In Mark's version, Simon is already called Peter, a nickname explained in Matthew 16:18-19.
The guidelines that Jesus gives to the Twelve puts a high premium on trust in God's providence and the goodness of men. While he allows his chosen men the luxury of a walking stick and sandals -- comforts for those travelling far -- he tells them not to bring a change of clothing and provisions for food. This last reminds one of the teaching about not worrying food and clothing but to work first for the kingdom of God (cf. Matthew 6:25-34; Luke 12:22-31). Could it be that the Sitz im leben of the texts from Matthew and Luke is the mission?
Finally, Mark 6:10-11 is a directive for the apostles to stay in the house where they are welcomed and to shake the dust off their sandals wherever they are not. Both these situations can perhaps explain two other sayings of Jesus: the one about the cup of cold water given to his own (Mark 9:41; Matthew 10:42) and the woes to Chorazin and Bethsaida (Matthew 11:21; Luke 10:13.