To find area $ A $ use formula:
$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$After substituting $ d_1 = 4 \sqrt{ 3 } $ and $ d_2 = 4 \sqrt{ 2 } $ we have:
$$ A = \dfrac{ 4 \sqrt{ 3 } \cdot 4 \sqrt{ 2 } }{ 2 }$$$$ A = \dfrac{ 16 \sqrt{ 6 } }{ 2 } $$$$ A = 8 \sqrt{ 6 } $$