Can someone me with the physics problem? : if you do 144 j of work to elevate a bucket of water, what is it’s final gravitational potential energy relative to its starting position?

The work you put into something is the energy it has afterward (neglecting friction and other so-called non-conservative forces).  This is called the work-energy theorem.  Think of objects in a gravitational field as "energy piggy banks".  If you put X joules of energy into it, that energy will be there as potential energy, stored for later.  So if you do 144J of work to elevate the bucket from an initial position, what ever it is initially, the final gravitational energy is 144J greater than before.

iowichie