If you are pushing two shopping carts at the same speed, the one that is twice as heavy (twice the mass) stores twice the 'movement energy' because you have to work twice as hard to get it moving at that speed.

The kinetic energy ($K.E.$) of an object is given by the formula $K.E. = \frac{1}{2}mv^2$. For object A, $K.E._A = \frac{1}{2}mv^2 = 100\,\text{J}$. For object B, the mass is $2m$ and velocity is $v$, so $K.E._B = \frac{1}{2}(2m)v^2 = 2 \times (\frac{1}{2}mv^2)$. Substituting the value of $K.E._A$, we get $K.E._B = 2 \times 100\,\text{J} = 200\,\text{J}$.

Always check if the variable changing is squared (like velocity) or linear (like mass) in the formula.