Explanation

The dimensions of angular momentum are $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ J = \left\lbrack {ML}^{2}T^{- 1} \right\rbrack$ When units of mass, length and time are doubled, than $\ \ \ \ \ \ \ \ \ \ \ \ \ J^{'} = \left\lbrack 2M(2L)^{2}(2T)^{- 1} \right\rbrack$ $\Rightarrow \ \ \ \ \ \ \ \ J^{'} = 4\left\lbrack {ML}^{2}T^{- 1} \right\rbrack = 4\ J$ Unit of angular momentum is quadrupled.