The curl of a vector field F = P(x,y,z)i + Q(x,y,z)j + R(x,y,z)k is given by:
Curl(F) = (∇ × F) = ( (∂R/∂y - ∂Q/∂z)i - (∂R/∂x - ∂P/∂z)j + (∂Q/∂x - ∂P/∂y)k )
For the given vector field F = 8xi + 9zj + 6yk, we have P(x,y,z) = 8x, Q(x,y,z) = 9z, and R(x,y,z) = 6y.
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