[jgrayczyk]

Which is a stronger base NaH or K-OtBU?

[rolnor]

NaH is stronger.

[Vidya]

Compare acidity of their conjugate acids.
In NaH , H^-  is the base and its conjugate acid is H₂
K O tert- Bu, base is tert -Butoxide  and its conjugate acid is tert-butanol .Now H on the oxygen of tert -butanol is more acidic then H of H₂ because of the difference in the electronegativity of H and Oxygen atoms.
Strong acids give weak conjugate base so if I compare   tert -Butoxide  with hydride ion then hydride  is stronger base.Or you can simply compare their pKb values.

[SamuelPi]

That makes sense thanks Vidya, I though NaH would be stronger.

[Babcock_Hall]

Which is a stronger base NaH or K-OtBU?

@OP,  Find the pK_a values and compare them.

[Babcock_Hall]

@OP, I just looked up the pK_a of H₂, and I found it to be 35.  See what you make of that.