1. I was puzzled what to do.

2. I was puzzle what I should do.

3. I was puzzled about what to do.
4. I was puzzle about what I should do.
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Which ones are grammatical?

#3 is best. #4 would be good if the verb were spelled correctly in past tense.

1. I was puzzled what to do.

Can we use this way, without 'about'?

It seems incomplete. It’s far better to have the preposition stated.

Out of the four sentences provided, sentence 1 and sentence 3 are grammatically correct.

1. I was puzzled what to do.
This sentence means that the person was confused or unsure about what action to take. "Puzzled" is an adjective modifying the subject "I," and "what to do" is a noun phrase functioning as the object of the verb "was puzzled."

2. I was puzzle what I should do.
This sentence is not grammatically correct. Here, "puzzle" is being used as a verb in the present tense, but it should be in the past tense to match the verb "was" in the past tense. The correct past tense form of "puzzle" is "puzzled," which should be used here.

3. I was puzzled about what to do.
This sentence is grammatically correct. It is similar to sentence 1, but the inclusion of the preposition "about" introduces a slight change in meaning. It implies that the person was confused regarding the specific topic of what action to take.

4. I was puzzle about what I should do.
Like sentence 2, this sentence is not grammatically correct. Here, "puzzle" is used as a verb in the past tense, but it should be in the past participle form "puzzled" to match the auxiliary verb "was" in the past tense. Additionally, the correct preposition to use in this context is "puzzled by" instead of "puzzle about."