For an English speaking person it is often hard to hear the difference between ы and и sounds.
If you remember the following spelling rule, you will be able to avoid some of the more common mistakes in your written Russian.
After consonants г, к, х, ж, ш, щ, ч, do not write the letter ы. Whenever an [ы] or [и] sound follows one of these letters, it is spelled и. This is the '7-letter spelling rule'
Practice reading words with consonants г, к, х, ж, ш, щ, ч followed by и.
гимн hymn, anthem
щи cabbage soup