Remember, displacement is the distance between his starting and finishing points.
If you draw this out, you will end up making a triangle. One side is the 6 meters to his bowl, the adjacent side is the 8 meters to his doghouse, and what you are trying to find is the missing side, which happens to be the hypotenuse.
Use the Pythagorean Theorem:
6^2+8^2=x^2
36+64=x^2
100=x^2
Take the square root of both sides, or just think 'what times itself equals 100?'
x=10
