It just means calculating $[δ_1,δ_2]X^\mu$ and $[δ_1,δ_2]\psi^\mu$... Perhaps you should first practice with susy invariance on a simple scalar multiplet, no doubt covered in your relevant course, and only then apply your expertise to this one.
Recall that $\delta \phi \equiv i[\bar \xi Q,\phi]$ for an arbitrary field $\phi$, boson or fermion. So δ may be thought of as a boson operator, and it is its commutators with other fields or operators that are meaningful, not its anticommutators. The fermionic nature of the supercharge Q is neutralized by the fermionic parameter ξ to yield a bosonic δ. Confirm this is so by comparing the l.h.s. of your transformations to the r.h.sides, and their respective statistics.