Castle Garenbrig enters the battlefield tapped unless you control a Forest.
{T}: Add {G}.
{2}{G}{G}, {T}: Add six {G}. Spend this mana only to cast creature spells or activate abilities of creatures.
Although the common lands have basic land types, they aren't basic lands.
Once the common lands (such as Mystic Sanctuary) enter the battlefield tapped, there's no way to untap them with a spell or ability to make their last ability trigger.
The mana generated by Castle Garenbrig's last ability can't be spent to activate abilities of creature cards that aren't on the battlefield.