Sailaja started from her house and walked 11 km towards the west followed by 20 km to her right. She then took a right turn to walk 6 km. Finally, she walked 8 km to her right. What is the distance between Sailaja's house and her destination?

Let's break down Sailaja's journey:

1. She started from her house and walked 11 km towards the west.
2. Then she turned right and walked 20 km. Since she was walking west, a right turn would lead her to the north.
3. She then took another right turn and walked 6 km. Since she was walking north, a right turn would lead her to the east.
4. Finally, she took one more right turn and walked 8 km. Since she was walking east, a right turn would lead her to the south.

Now, if we look at the path, the first and the third segments (11 km west and 6 km east) are in opposite directions. So, the effective distance in the east-west direction is 11 - 6 = 5 km (west).

Similarly, the second and the fourth segments (20 km north and 8 km south) are in opposite directions. So, the effective distance in the north-south direction is 20 - 8 = 12 km (north).

The distance between Sailaja's house and her destination is the straight-line distance between these two points. We can use the Pythagorean theorem to calculate this, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

So, the distance is sqrt((5 km)^2 + (12 km)^2) = sqrt(25 + 144) = sqrt(169) = 13 km.

So, the distance between Sailaja's house and her destination is 13 km.