Momentum, or impulse (the change in momentum) of an object is its "quantity of motion." It is defined as the product of the mass `m` of an object and its velocity `V.` As such, momentum is actually a vector quantity.
When two bodies move towards one another and have a collision, the object which has a greater momentum hits harder. Also, for a closed system of bodies, momentum is conserved.
Kinetic energy is a scalar quantity which is defined as `(mV^2)/2.` It is also a measure of a quantity of a body's motion. Energy (not only kinetic but all types of energy) is also conserved in a closed system.
Now if `mV` is increased `4` times (and mass `m` remains the same), this means `V` is increased `4` times: `V_1=4V.` Therefore, kinetic energy becomes `(mV_1^2)/2=(m(4V)^2)/2=16*(mV^2)/2.`
So, we can state that kinetic energy is increased `4^2` = 16 times. This is the answer.