How would you balance the chemical equation by adding coefficients as needed?
#NaOH(aq) + NaNO_2(aq) + Al(s) +H_2O(l) -> NH_3(aq) + NaAlO_2(aq)#
You have described a redox process, for which 1/2 equations are the standard approach.
Aluminum metal is oxidized to aluminate,
This is balanced with respect to mass and charge.
Nitrite anion is reduced to ammonia:
Again, this is (I think) balanced with respect to mass and charge, and is therefore reasonable.
I think this is balanced; but don't trust my arithmetic. If you need help with individual steps, ask for it. All I have done is write 2 half equations. Aluminum is oxidized to
Note that I think basic conditions are required, not acidic condtions. And we could resolve this by adding
Charge is balanced; mass is balanced, so I'm happy.