Correct spelling, explanation: eight is quite a problematic word in terms of spelling and is often confusing for English learners due to its pronunciation. The practice of replacing the hard H sound with the letter combination -gh- was a common habit among Middle English scribes, particularly when preceding the letter -t-. So, ght is the correct way to write this sound, similarly in fight, night etc. Therefore eigth is incorrect and eight is the correct spelling.

Definition of eight:
numeral, a cardinal number between seven and nine
My son turned eight years old yesterday, and we celebrated with a big birthday party.
The recipe calls for eight cups of flour to make a delicious batch of homemade bread.

Phrases with eight:
1. To be behind the eight ball
Being behind the eight ball means finding oneself in a difficult or disadvantageous situation. This idiom derives its origin from the game of pool, where the eight ball is the last ball that should be pocketed. If this ball is unintentionally pocketed too soon, the player loses, making it a situation to be avoided.
He’s really behind the eight ball with all those pending assignments.
2. One over the eight
The expression one over the eight means to be drunk. It dates back to the 1920s in the UK, suggesting that an individual can consume eight pints of beer without experiencing the effects of being drunk.
Today I got so embarrassed when I realised I had been one over the eight last night and talked stupid things in front of my boss.

Incorrect spelling, explanation: this spelling is incorrect, because the word eight uses ght sound, which occurs in other words too, such as light or fight. Middle English scribes often had the habit of using the spelling -gh- instead of the hard H sound, especially when it came before the letter -t-. This is why eigth is incorrect and probably mistaken with a suffix -th. The only correct spelling here is eight.