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Suppose I am trying to tell someone, how much distance google maps shows if we take car or on foot. How would I say this?

"My house is 10KM from here by car and 8 KM by/on foot."

I think "by" is used for means of transport but is it correct to use this here or "on" foot sounds appropriate?

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You can say "by car" and "on foot".

However, the following are usual and more idiomatic:

My house is a 10-kilometer drive from here.

My house is a 8-kilometer walk from here.

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You can use both; although technically, on is more accurate and common.

In the context of your sentence, by may be used for a foot as a tool used for movement, and on -- for a foot as the part of a body on which this body moves, which, in my opinion, doesn't make any difference.

For a possibility of using "by foot" you may also see here.

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