what is the rule for why "achieved' is spelled that way instaed of "achieveed"?

I don't know of any rule for that -- except we don't pronounce this word with a long e between v and d.

Are you looking for this rule:

i before e except after c, except when the sound is ay as in neighbor and weigh.

The rule for why "achieved" is spelled that way instead of "achieveed" is related to the doubling of letters in certain words. When adding suffixes like "-ed" to a base word, you need to consider the ending of the base word and the syllable stress.

The general rule is that if a base word ends in a single vowel followed by a single consonant and the last syllable of the word is stressed, the final consonant should be doubled before adding the suffix "-ed."

In the case of "achieve," it follows this rule. The word "achieve" ends with a single vowel "e" followed by a single consonant "v" and the stress is on the last syllable. So, when adding the suffix "-ed" to make it past tense, we double the final consonant "v" and write it as "achieved."

This rule ensures that the stress remains on the same syllable and helps maintain the pronunciation of the original word. However, it's important to note that English spelling rules can be complex and have exceptions, so it's always helpful to consult a reliable dictionary or style guide for specific words.