I need help walking through the full set up and process of b

I need help walking through the full set up and process of balancing the equation. Here is the question:

Solid aluminum hydroxide is placed in a test tube and mixed with water. The contents of the test tube are added to a solution of nitric acid and are thoroughly mixed. The coefficient of water in the balanced molecular equation is:

A. 1

B. 2

C. 3

D. 6

E. Water is not formed in this reaction.

Please help me balance the equation and include which substances are solid liquid aqueous or gas. Thanks a ton!

Solution

Al(OH)3 + HNO3 ----> H2O + Al(NO3)3

step 1 balance Al atoms............balanced

step 2 balance N atoms.

Al(OH)3 + 3HNO3 ----> H2O + Al(NO3)3

step 4 balance O atoms

Al(OH)3 + 3HNO3 ----> 3H2O + Al(NO3)3

step 5 balance H atoms........Balanced

so final reaction

Al(OH)3 + 3HNO3 ----> 3H2O + Al(NO3)3