The abbreviation for 'for example' is 'e.g.', an abbreviation for the Latin 'exempli gratia', meaning 'for the sake of example'.
You might say,
'We're considering buying a large breed of dog, e.g., a German Shepherd, or perhaps a Malamute.'
'Meat stews are frequently cooked with root vegetables, e.g., carrots, turnips, and so on.'
The term is usually written with the two full stops; without them 'eg' can look like a misprint, and 'eg.' looks clumsy. It is usually written with a following comma, depending on the writing style.
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