As common types of bets that can be placed on a horse race with six horses are:

1. **Win bet**: This 1️⃣ is a bet on a horse to win the race. If the horse comes in first place, the bettor wins 1️⃣ the amount stated in the odds.

2. **Place bet**: This is a bet on a horse to finish either first or 1️⃣ second. If the horse comes in first or second place, the bettor wins the amount stated in the odds.

3. **Show 1️⃣ bet**: This is a bet on a horse to finish either first, second, or third. If the horse comes in 1️⃣ first, second, or third place, the bettor wins the amount stated in the odds.

4. **Across the board bet**: This is 1️⃣ a combination of win, place, and show bets. The bettor bets on a horse to win, place, and show. If 1️⃣ the horse wins, the bettor collects on all three bets. If the horse comes in second, the bettor collects on 1️⃣ the place and show bets. If the horse comes in third, the bettor collects on the show bet.