Question

what is the balanced equation of H + [Al(OH)4]

Answer 1

I don't understand the equation you have written. Aluminium hydroxide is

Al(OH)3; is that is what you mean?

Are you trying to write the equation for a hydrogen storage device based on aluminium?

Al(OH)3 + H2 <-> Al + H2O

which you can have a go at balancing.