To Escape Something
To Avoid Something
transitive verb, ichidan verb
You are going to excuse yourself from the situation, and in order to do that, you have to escape from the person / thing trying to hold you there in order to avoid them.
In order to do that, you jump inside your man(u) car (まぬか) which is a car for a tough man(u) that needs to drive fast, just like you.
We managed to avoid the worst possible outcome of bankruptcy.
I'll do anything to escape execution.
We avoided serious injury because we sat in the back seat and wore our seat belts.