This is a speech from Shikamaru, a character from Naruto manga.
The nuance is, his very first mission as a leader ended in a giant failure with the rest of his team severely hurt and he only got a broken finger.
The above image is the moment that he vows to not fail again, which can be translated as something like:
Next time for sure... I'll carry out the mission perfectly!
But what makes me confused here is the phrase:
I was taught that,
show something (to somebody), but what does Shikamaru show here?
I have also looked up
熟す (こなす), which means
こなしてみせます just does not make any sense to me.