For example, you say to me
My eye is sick
But I heard
My I is sick
I have read a 'homonym' article but it just show the words that have same sound on speaking. How to distinguish one word with another that has the same sound?
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Being able to distinguish homonyms in speech is something you need to practice. Once you get familiar with English, you'll be able to understand which word people mean based on the context.
Bob says to Anne
I had a great vacation last fall
There are multiple meanings for fall (even written the same way): 1. the season Fall, between summer and winter; or 2. to fall, where you trip or otherwise make contact with the ground in an unpreferred way.
Anne knows that you cannot have a vacation while falling down, but you can have a vacation during the season of fall. She understands that Bob means that he went on a vacation during this season.
In summary: There is no definitive guide to understanding which word people mean while speaking, while you learn English you will understand that some words are more probable in a certain context, compared to others.