Suppose a cart is being moved by a certain net force. If the net force is increased by a factor of 6.8, by what factor does its acceleration change?

If the net force is increased by a factor of 6.8 its acceleration also increases by a factor of 6.8.

This is based on Newton's second law of motion where this formula applies:

Force = Mass * Acceleration

Since mass here is a constant; force therefore varies proportionately with acceleration.

So increasing force by a factor of 6.8 directly increases acceleration of the cart by the same factor.