You apply a force of 10.7 N on a 4.1 kg object, pushing it horizontally across a surface where the coefficient of kinetic friction is 0.34. (a) Determine the frictional force acting. (b) Determine the object's acceleration?

Friction Force=(FN) * (Coefficient of kinetic friction)

FN=Normal force

And the Normal force is perpendicular to the surface, in this case it's the gravitational force (or weight of the object) and is calculated by FN=Mass*g ,

Now you have the normal force and coefficient of kinetic friction, it should be pretty straightforward to calculate the frictional force.

and for the second part : (horizontal force)-(friction force)=m*a

the result for acceleration can be both positive and negative.

since this might be your homework I didn't write the numbers, if you encounter a problem in this solution go ahead and ask.