To find leg $ b $ use formula:
$$ \sin \left( \beta \right) = \dfrac{ b }{ c } $$After substituting $ \beta = 45^o $ and $ c = \sqrt{ 6 } $ we have:
$$ \sin( 45^o ) = \dfrac{ b }{ \sqrt{ 6 } } $$ $$ \frac{\sqrt{ 2 }}{ 2 } = \dfrac{ b }{ \sqrt{ 6 } } $$$$ b = \frac{\sqrt{ 2 }}{ 2 } \cdot \sqrt{ 6 } $$$$ b = \sqrt{ 3 } $$