When I was 4 years old, my sister was half my age.    Now my sister is 12  years old. How old am I

You are 14 years old.

Here's the explanation:

When you were 4 years old, your sister was half your age. That means she was 2 years old. Since 2 squared equals 4, you have to square the 4 to get 16. You then multiply 16 by 2 (her original age) to get 32. After that, you subtract 4 (your original age) from 32 to get 28. Since your sister is 12 right now, you subtract 12 from 28 to get 16. Your sister’s starting age in this calculation was 2, not 0, so you subtract 2 from the 16 to account for those first two years. The resulting number is 14. Therefore, you're 14 years old. Simple.

I know what you're thinking. You're thinking,

“That doesn't make any sense at all. My IQ went down just from reading that. You're an idiot.”

You’re right.

For real though:

When you were 4, half of your age was 2. That means you were 2 years older than your sister. You'll always be 2 years older than her, so if she's 12, you have to be 14.

Just kidding.

I was closer that time, but not quite.

If her birthday is the exact same day as yours, then you're definitely 14. But if her birthday happened this year and yours didn't happen yet, you could be 13. Or if your birthday happened already and hers didn't, you could be 15. But if your question refers to exactly 10 years before today, then you're 14.

I hope that made sense.