The idea is similar to the ones for one-step methods I think. First of all note that the exact solution of the Dahlquist test problem $y' = \lambda y$, $y(0)=1$, is $y(x) = e^{\lambda x}$. Since this solution is bounded for $Re(\lambda) < 0$, we expect the same behavior for the numerical solution in this case.
By applying multiple steps of a one-step method, such as forward Euler, to the problem, $y_{k+1} = (1 + h \lambda) y_k = ... = (1 + h \lambda)^{k+1} y_0$. So we have expressed the $k+1$-th step using the initial value. Then taking the absolute value it becomes obvious that we need $|1…