There is no way to restore a hint you played by mistake.
To earn free hints, you can do the following:
Fill the hint-o-meter. You fill the hint-o-meter by completing levels and collecting energy. It takes 10 energy to fill!
Playing the Daily Spinner. You can get varying amounts of energy or if you are luck a whole hint from a spin.
Completing special seasonal events. Rewards are shown in the rewards ladder during the event.
Inviting a friend to play WordBrain 2, once the friend installs the game from the link you shared and starts playing, you will receive more free hints.
Keep an eye out for hint pack sales and special seasonal campaigns!