To find incircle radius $ r $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 6 } $$After substituting $a = 6\, \text{cm}$ we have:
$$ r = \dfrac{ \sqrt{ 3 } \cdot 6\, \text{cm} }{ 6 } $$$$ r = \dfrac{ 6 \sqrt{ 3 }\, \text{cm} }{ 6 } $$ $$ r = \sqrt{ 3 }\, \text{cm} $$