To find height $ h $ use formula:
$$ h = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $a = 6\, \text{cm}$ we have:
$$ h = \dfrac{ \sqrt{ 3 } \cdot 6\, \text{cm} }{ 2 } $$$$ h = \dfrac{ 6 \sqrt{ 3 }\, \text{cm} }{ 2 } $$ $$ h = 3 \sqrt{ 3 }\, \text{cm} $$