In [Adámek, Rosický - Locally presentable and accessible categories, p59], the authors state in exercise 1.b(2) for infinite cardinals $\lambda_0, \lambda$
if $\lambda_0$ is the cofinality of $\lambda$, then $\lambda$-directed colimits can always be reduced to $\lambda_0$-directed ones. In contrast, if $\lambda_0<\lambda$ are two regular cardinals, verify that $\lambda$-directed colimits cannot be reduced to $\lambda_0$-directed ones: find a category with $\lambda$-directed colimits which fails to have $\lambda_0$-directed colimits.
What exactly do they mean by can be reduced here?
I see that every $\lambda$-directed set is $\lambda_0$-directed for $\lambda_0 \leq \lambda$, the converse being false in general. If $\lambda$ is singular, every $\lambda$-directed set is furthermore $\lambda^+$-directed where $\lambda^+$ is the cardinal successor (always regular).
Thus, a category that has all $\lambda_0$-directed colimits also has all $\lambda$-directed ones, and for $\lambda$ singular, you have $\lambda^+$-directed ones iff you have $\lambda$-directed ones.
But that's not the direction implied by can be reduced. And for example, the poset $\aleph_1$ does not have all $\aleph_0$-directed colimits, but it has all $\aleph_2$-directed and $\aleph_\omega$-directed ones, even though $cf(\aleph_\omega) = \aleph_0$.
I hope you can clarify what is there to prove in the exercise.