To make a staircase 117 inches high with just the runs, how far do I need to measure from the wall to the last tread at the base of the stairs?

You’re missing some information in your question.

In order to answer this question you need to have decided the number of treads and risers. At 117″ you can have risers at about 8″, but this is steep for most people (15 risers). Most residences are around 7″ (17 risers) to 6″ (20 risers).

You have one less tread than risers. We aren’t going to count the nosing (the part that sticks out past the riser). Again 10″ can work, but most people don’t like them. 11″ to 12″ for treads work well in most homes.

So, take your riser count. Minus one. Multiplied by your tread size.

You’ll get somewhere between 140″ (very steep) to 228″ (easy to walk up).

Also, be aware that there are a number of different ways to size stairs, and that this is just one that easier to explain and understand.