Based on evidence drawn from both Scripture and Tradition (Catholic or Orthodox), is Christ peccable, or impeccable?
This is a question that has been discussed in many forums almost since the time of Christ.
First, according to Merriam-Webster, peccable means "liable or prone to sin or susceptible to temptation." The Oxford dictionary defines it as "capable of sinning."
According to scripture:
Hebrews 4:15 - "For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yet without sin."
The root cause of the argument is simply the fact that Jesus was truly human and also truly divine. As a human he was susceptible to temptation but because of his divinity he was sinless.
The question of could Christ have sinned, if he wanted to, can never really be answered definitively.
Tradition holds that Christ is impeccable. Because he was free of original sin and therefore internal temptation, his divinity meant that he could never have given in to external temptation.
As I said, this question has been discussed for centuries and is still being discussed today. You can see the links I've attached for more detailed discussion.
Hope this helps.