The placement of teams in each quarter on knock-out basis can be done through the following procedures:

1. Random Selection of Teams: The first step is to randomly select the teams that will participate in the tournament. This can be done through a draw or a computer algorithm that randomly selects the teams.

2. Seeding: Once the teams have been selected, the next step is to seed them based on their performance in previous tournaments or their current ranking. The top-ranked teams are seeded higher and placed in separate brackets to avoid facing each other in the early rounds.

3. Bracket Creation: The third step is to create the brackets for the tournament. This is done by dividing the teams into four groups and placing them in each quarter of the bracket.

4. Matchups: The fourth step is to determine the matchups for each round of the tournament. This is done by pairing the teams in each quarter against each other. For example, the first seed in one quarter will play the eighth seed, the second seed will play the seventh seed, and so on.

5. Knock-out Rounds: The teams will then play in a knock-out format, with the winner advancing to the next round and the loser being eliminated from the tournament. This format continues until there are only two teams left, who will then play in the final to determine the winner.

6. Tiebreakers: In the event of a tie, there are several tiebreakers that can be used, such as goal difference, head-to-head record, or a penalty shoot-out.

7. Re-seeding: In some tournaments, such as the FIFA World Cup, the teams are re-seeded after each round to ensure that the top-ranked teams do not face each other too early in the tournament.

Overall, the placement of teams in each quarter on knock-out basis involves a combination of random selection, seeding, bracket creation, and match-ups, with the ultimate goal of determining the best team in the tournament through a series of knock-out rounds.