Statement-1: Occasionally +2 and +4 oxidation states of lanthanides are obtained. 

Statement-2: Empty, half-filled or filled f-subshell are extra stable

Lanthanides can sometimes reach their +2 and +4 oxidation states. F-subshells are more stable whether they are empty, half-filled, or full.

These are demonstrated by the elements that, after losing two or four other components, acquire a stable configuration. 

The lanthanide exhibits the +2 oxidation state when its arrangement is $5{\mathrm{d}}^{0}6{\mathrm{s}}^2$, which makes it simple to lose 2 electrons.

The +2 and +4 oxidation state occur if $f^0,f^7,f^{14}$  electronic configuration occur