The answer is 7 3/4 inches.
I noticed the word "train" in the problem and I knew I had to help you! :)
Why not draw the graph of y=|x|? It has a v-shape, and the vertex is at (0,0).
The graph of f(x) = |x| - 3 looks exactly the same, EXCEPT that the whole graph of |x| is shifted 3 units downward. The smallest value that y can have is therefore -3.
Can you now figure out the range of f(x)?
You should scan it on this app:)