Question 13119
Assume you know where they meet. It is at point M. They take the same amount of time (x) to travel to point M.
She travels at 2 mi/hr. In x hours she will travel 2x mi. This is the distance M. So, 2x = M.
He travels at 3 mi/hr. In x hours he will travel 3x mi. This is the distance from where he is to M. But he is already at 4 mi. (That's how far apart they are when they start!) So the distance he travels to get to M is 4-M. [Can you see why?]
So, 3x = 4-M.
Now we solve for x.
2x = M
3x = 4 - M
3x = 4 - 2x [substituting 2x for M]
5x = 4
x = 4/5
Check: In 4/5 of an hour she will travel 8/5 mi.
In 4/5 of an hour he will travel 12/5 mi. 
The total distance they traveled is 8/5 mi. + 12/5 mi. = 20/5 mi. = 4 mi.