ok im gonna keep this brief...
im an "explorer" gamer meaning i tend to do all side things and search every area of the map before getting too much into the story....with that said,
ive leveled up in fallout new vegas as far as i can go and did not happen to make my explosive skill high enough to finish the mission in vault 19(need 60 for how i want to complete it)
even with the implant and skill books(i dont steal by the way so thats ruled out) i still can't get it past 60.
Posting this in the correct forum would be a good start. This is the fallout 3 forum not he New Vegas one.
Secondly you didn’t give what your explosives skill was to begin with. Telling us you need to get it to 60 is pointless without telling us where you’re starting from.
Have you read all the Duck and Cover books? You say you don’t steal, but hey that’s your choice. Its not like the NPC you steal it from really cares. Absinthe can raise your explosives skill, depending on your survival skill. Also the raider blast master helmet will raise it +5.
Rather than coming here and asking simple questions like this, its much faster to read the appropriate articles. The one on explosives skill http://fallout.fandom.com/wiki/Explosives should give you all the answers you need.