Let's put this on the usual Cartesian grid just so we can talk about it without drawing a picture. We'll use map conventions, right is east, up is north.
The ball starts at (0,0). 10.3 feet northwest means we have an isosceles right triangle whose diagonal is 10.3 feet. It's isosceles because northwest means equal parts north and west.
The sides of these triangles are in ratio

so the coordinates after the first putt are

The negative sign indicates west, which doesn't really matter for this problem. The distance from the origin to this point is 10.3 as required.
Now a second putt of 3.8 feet north puts us at

The squared distance to the origin is exactly

A little calculator work tells us

Third choice.
The answer to your question is y=1
Answer:
23.44%
Step-by-step explanation:
The probability of getting a 4 on the first 2 throws and different numbers on the last 5 throws = 1/6 * 1/6 * (5/6)^5
= 0.01116
There are 7C2 ways of the 2 4's being in different positions
= 7*6 / 2 = 21 ways.
So the required probability = 0.01116 * 21
= 0.2344 or 23.44%.