1. This is the way he did it.
2. This is how he did it.
3. This is the way in which he did it.
4. This is the way by which he did it.
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Are they all grammatical? Can we use 'by' instead of 'in'?
Yes, all of the sentences are grammatically correct. However, there are slight differences in meaning and usage.
1. "This is the way he did it." - This sentence is simple and straightforward, stating that there is a particular way in which he did something.
2. "This is how he did it." - This sentence is also common and idiomatic. It means the same as the first sentence; it just uses the word "how" instead of "the way."
3. "This is the way in which he did it." - While grammatically correct, this sentence sounds a bit formal and less commonly used in everyday conversation. It emphasizes that there is a specific manner or method in which he did something.
4. "This is the way by which he did it." - This sentence is grammatically correct but less commonly used. It suggests that there is a means or mechanism (using the word "by") through which he did something. While technically correct, it may sound more formal or old-fashioned compared to the other sentences.
Regarding the use of "in" versus "by," generally, "in" is more commonly used to indicate the manner or method, while "by" is used to indicate the means or mechanism by which someone did something. However, in everyday conversation, "in" is more frequently used and is generally considered more natural.