Time for my obligatory wade into the middle of a religious battle.
>I need a little help in understanding the solution reflected in verse 20-22.
>So give back to Caesar what is Caesar's, and to God what is God's.
It means give Caesar the money he wants. Ultimately, the money doesn't mean anything, he just has his face imprinted on it.
And to give to God what is God's, IE your spirit, your soul. Essentially it translates into 'give Caesar his money back and come follow God'.
John mentions 'silver and gold I do not have', and 'what I do have, I give you' to the poor beggar. The thing he has is Christ's Spirit.
Now, if you don't mind, I'm going to wade back out again before some religious fanatic misinterprets what I've written (again) and forces me into paragraphs long stand-off establishing something that is fairly evident to everybody.