Answer
In all three cases there is a net force to the right so the spool moves to the right, by Newton's second law.
Work Step by Step
Try it and see!
Leftmost picture: the string tension produces a net torque around the spool's point of contact with the table. The spool pivots clockwise about that point and rolls to the right.
Middle picture: the tension’s line of action extends straight through the point of contact. The lever arm is zero. The pulling force produces no torque. There is an unbalanced force component pointing to the right. The spool slides to the right, but does not rotate.
Rightmost picture: the analysis is the same as for the leftmost picture; the spool rolls to the right.
