See, pls, the offered explanation:
1. equation for sphere has a form: (x-x₀)²+(y-y₀)²+(z-z₀)²=r², where x₀, y₀ and z₀ are points of center (4;3;6), and r - radius of sphere.
2. according to the task the sphere must be in the 1-t octant and must be the largest, it means that among all the possible radius (4-0=4; 3-0=3; 6-0=6) need to choose the shortest one. r=3.
3. summary: (x-4)²+(y-3)²+(z-6)²=3.