Using a simple frame or just bolding for the box
Key Points:
The most common oxidation state for lanthanides is +3.
Extra stability is associated with empty (f$^0$), half-filled (f$^7$), and fully-filled (f$^{14$) f-subshells.
Eu ([Xe] 4f$^7$ 6s$^2$) readily forms Eu$^{2+$ ([Xe] 4f$^7$), making +2 a common stable state for Eu.
Gd ([Xe] 4f$^7$ 5d$^1$ 6s$^2$) readily forms Gd$^{3+$ ([Xe] 4f$^7$), making +3 the very stable and common state for Gd.