You are solving for the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS, and isolate the variable.
First, subtract 2 from both sides.
5x + 2 = 12
5x + 2 (-2) = 12 (-2)
5x = 12 - 2
5x = 10
Isolate the variable, x. Divide 5 from both sides.
The verticall intercept is the value of H
when t=0.
It's 4 in this equation.
It's that "several inches" of water that were in the bucket when the rain was ready to start.