The rules says you can do the discard 4 cards and draw 4 cards twice. If you are unable to play the 2nd time around, your turn is over and you don't get to play a card that turn.Wait, wait. Draw only once, but show twice.
Let's look at the complete paragraph
If a player cannot place any of his 8 cards, he shows them to his opponent to prove he cannot place a card. If he can place a card, he must. If not, he may discard up to 4 cards (choose how many first) and draw the same number from the supply. If he now can place a card, he does. If not, he again shows his cards to his opponent to prove this. If he can place a card, he must. If not, he ends his turn without placing a card.