The first step is to write and balance the chemical equation. it is
`X*H_2 + Y*CO_2 = Z*CH_4 + W*H_2O.`
To balance it, consider equations for `H,` `C` and `O:`
`H:` `2X = 4Z + 2W` (thus `X = 2Z + W`),
`C:` `Y = Z,`
`O:` `2Y = W.`
The irreducible solution is `Y = Z = 1,` `W = 2Y = 2` and `X = 2Z + W = 4,`
`4H_2 + CO_2 = CH_4 + 2H_2O.`
The second step is to create and solve a simple proportion: `4` moles of hydrogen gas `H_2` are required for each `2` moles of water, and `h` moles of hydrogen is required for `99.1` moles of water.
The proportion is `4 : 2 = h : 99.1,` thus `h = 99.1*4/2 =198.2` (moles). This is the answer.
Note that this reaction also requires a catalyst and high temperature.