In Mark 3:14-15, we are told why Jesus chose the 12 apostles:
And he appointed twelve (whom he also named apostles) so that they might be with him and he might send them out to preach and have authority to cast out demons.
However, they didn’t do all these things immediately. Some training was necessary before they could begin to preach, for example.
Their first preaching mission is described in Mark 6:
And he called the twelve and began to send them out two by two, and gave them authority over the unclean spirits. (Mark 6:7)
So this was when they actually received the authority over unclean spirits (also called demons).
In other words, Jesus didn’t give the power to drive out demons twice. The first passage above described what would later happen, and the second passage described the time when Jesus first gave them this power.