For which of the following Lanthanide +II and +III oxidation states a…

Lanthanides show variable oxidation states. The most stable oxidation state of Lanthanides is $+3$. They also show $+2$ and $+4$ oxidation states due to the presence of either half filled or completely filled or empty $4f$ sub shell.
Due to stable half filled configuration $Eu$ shows $+2$ configuration.
₆₃Eu : [Xe]4f⁷6s²