Why do I only need the first 4 letters for each word in a mnemonic seed phrase?
Bitcoin Improvement Proposal (BIP 39)
Your 12-24 recovery seed phrase most likely comes from the Bitcoin Improvement Proposal: 39 (BIP 39). BIP 39 is the use of a mnemonic phrase -- a group of easy to remember words -- to serve as your back up recovery in the event your wallet becomes compromised.
These words are pulled from a specific list of 2048 words. In this list, the first 4 letters are unique to each word. (including the words that only have 3 letters -- think of a "blank" as a letter)
In other words, there are no two words in this list with the same first 4 letters.
That means if you have the first 4 letters, you know the rest of the word by looking for those first 4 letters in the BIP39 list. Some wallets will even fill in the rest of the word once the first 4 letters are entered.
As an authoritative source, the BIP 39 documentation specifically states the following:
To further test this fact, below is an exercise using Google Sheets to count the number of unique words in the BIP39 English wordlist using only the first four letters of each word. We ensure that it also equals to 2048. This is known as a mnemonic frequency analysis.
This feature does not only apply to the English wordlist. It also applies to the Spanish, French, and Italian wordlists. See the BIP 39 documentation for special consideration of wordlists.
Lighting Network (AEZeed)
If you're using a wallet compatible with Lightning Network, it uses a different seed scheme known as AEZeed. But, it uses the same wordlist as BIP 39. Thus, the same feature: unique first four letters for each word, applies.
Satoshi Labs Improvement Proposal (SLIP 39)
But, this wordlist also has the same design in which the first 4 letters are unique to each word.
Per the SLIP 39 documentation, "All words begin with a unique 4-letter prefix."