Does sodium metal react with potassium hydroxide solution?

No. It would be a displacement reaction and this only works if the metal is higher in the activity series than the one it wants to displace. Given that potassium is the highest ranked metal (sodium second), there should be no reaction. Look up activity series for more information.

Na metal will react with a KOH solution because it reacts with the H2O of the solution. It does not displace K^+ as Supa has written.
2Na + 2H2O ==> H2 + 2NaOH

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