You can use both start and begin for an activity. "Begin" is more formal than "start":

I started playing the piano when I was 8 years old.

What time does the meeting start?

He's beginning to read more advanced books in English.

We left the park when it began to rain.

When you turn on a car or vehicle, use "start":

I had to call a mechanic because my car wouldn't start.

In general, begin is used for more formal and more abstract ideas:

Scientists are studying how life began on earth.

World War II began in 1939.

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