The question stipulates non-negative numbers, so only one of Rom's sets is valid. If the question required integer solutions then (0,0,0, 2) is also a solution. However, it specifies real numbers (not necessarily integers), so there may well be other solutions, but so far I haven't put any thought into what those might be!
The only other one I can think of is (0, 0, √2, √2).
Total energy (TE) = Kinetic energy (KE) + Potential energy (PE)
KE = (1/2).m.v2, where m is mass and v is velocity
PE = m.g.h, where g is gravitational acceleration and h is height (above pool surface).
Calculate TE at diving platform (you have already calculated the KE there).
Work out the PE at the point 6metres below the platform.
Then, because TE is conserved, you can set (1/2)mv2 + PEat6metresbelowplatform= TE, where v is now the velocity at 6m below the platform. This v is the only unknown, so you can rearrange the equation to find it.
Incidentally, you should really give your results with units: Joules for energy, metres/sec for velocity.