Which of the following is the correct sentence:
- I would rather do it myself.
- I would rather did it myself.
When I meant to say that I don't know how to do this work otherwise I am well enough to do it myself.
Would rather is an idiom. In this idiom, would can take a bare infinitival clause as a complement:
I would rather [ do it myself ] .
Here, do is a bare infinitive. That means it's like to do, but without the infinitive marker to.
It's possible for this complement to have a subject, particular when it's a different subject than in the main sentence:
I would rather [ he do it himself ] .
This sentence is also okay.
In this idiom, would can also take a finite clause as a complement:
I would rather [ he did it himself ] .
But the idiom requires that a finite clause complement be in the past tense:
*I would rather [ he does it himself ] . (ungrammatical)
This sentence is non-standard, although some native speakers might say it anyway.
But this finite clause must have a subject, so you cannot say the following:
*I would rather [ did it myself ] . (ungrammatical)
"I would did" is incorrect because the syntax is:
[subject:I] [auxiliary:would] [verb:did]
The problem is that both the auxiliary verb "would" and the main verb "did" are in the past tense. "Would" is the past tense of "will", and "did" is the past tense of "do".
In English, only one verb may carry the past tense. If a sentence has an auxiliary verb, then the past tense is always carried by the auxiliary and the main verb is either the plain present as the combination "will do" (future + present) or a past participle, as in the combination "had done" (past + participle).
So it has to be "would do" (past + plain) and not "would did*" (past + past).
There are dialects of English which past tense on multiple verbs in the same sentence. If you hear someone using "did went", that is a dialect.