Finding Vout of a Transformer
I'll assume that multiplying by 8 was a typo, and that you meant 6, as your original ratio was 1:6.

The usual way to read it is the first number represents the primary, the second the secondary, so in your example you would have 120v output.

However, I know many people who describe all transformers in the style N:1, where N is larger than 1, and then describe which way round it's connected.

When it matters, you need to double check what the ratio means. It matters in simulators, check the simulator is using the convention you expect. It matters if you are plugging the transformer into the wall, and then accidentally going to touch the secondary!

The length and thickness of wire will not change the ratio, but they will affect the output voltage slightly when on load, due to differing voltage drops in the wire with the load current (and primary current!)