Doubling down 8v3 (player 8, dealer 3) is not proper basic strategy.
Go here:
http://www.blackjackinfo.com/bjbse.php
Scroll down. To the bottom left, there's an area to choose the game/rules you play (decks, rules such as if dealer hits or stays on soft 17, if you can double after split, surrender, etc.). Click on "get strategy" and memorize that table.
Most casinos deal two cards to the dealer, one up and one down. From what you posted, it looks like you only gave the dealer a single card. If "US Peak" is part of the rules, that means that the dealer looks to see if there is an Ace as the bottom card if he has a ten up, and also checks for a ten as the bottom card if he has an Ace up.
I'm not sure what you're asking about if you dealt properly.
Dealer had a 3, then got a 3 card (totaling 6). Got another 4 card, totaling 10. He drew another 8 card and totaled 18, at which point he would stop drawing cards because he has a hard 17 or higher.
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