How long would it take to travel 4 light years in a space shuttle?

Depends on how fast the shuttle was going. If it was traveling the speed of light, then only four years. The averal orbital velocity of the space shuttle is 17,000 - 18,000 mph. So let's see...

Light travels at 186,000 miles per second, 3600 seconds in an hour, 24 hours in a day, 365.25 days in a year.

So light travels 5,869,713,600,000 miles in a year

In four years it would travel 23,478,854,400,000 miles.

It would take the Space shuttle traveling an average of 18,000 mph 1,304,380,800 hours to reach that distance, which is 54,349,200 days or 148,800 years