The high-low game is the some one you are familiar with if you have ever played the Gameboy Advance versions of Mineral Town. Before you can play the same game in the DS version, you will need to find at least 60 Harvest Sprites so the Harvest Goddess can be released from her stone form.
Afterwards you need to give the Goddess gifts by tossing them into her pond. It will take 20 gifts before she decides that she would like to play the High-Low game with you. Make sure you have nothing equipped in the Tool (red) slot in your rucksack!
The Goddess will display a number on the screen and then ask if you think the next number will be higher or lower than her current number. If the next number she displays matches what you guessed, you will get to play again. If the number is the same than you get to play again anyway. The game will end if you make any errors.
You need to win at least 2 times before you will receive a prize. Up to 10 wins will earn you a random type of seeds. Anything past 10 will level up that same seed crop. For example, if you won 14 times then you might receive 8 bags of Turnip seeds that are level 4.
After your 1st try at the game, it will only take 10 gifts before she will want to play with you again. If you forget to remove any tools from your rucksack and play with her, any prizes you might have won will be forfeited. The Goddess needs your tool slot empty so she can give you the bags of seeds.