These are the chemical equations for the reactions:

FeCl3 (Iron (III) Chloride) --> Fe(NO3)3 (Iron (III) Nitrate)
FeCl3 + 3HNO3 → Fe(NO3)3 + 3HCl

Fe(NO3)3 (Iron (III) Nitrate) --> Fe(OH)3 (Iron (III) Hydroxide)
Fe(NO3)3 + 3NaOH → Fe(OH)3 + 3NaNO3

Overall reaction:
FeCl3 + 3HNO3 + 3NaOH → Fe(OH)3 + 3NaNO3 + 3HCl