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Differentiate w.r.t. d
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\frac{2c^{2}\times 4d^{2}}{9d\times 6c}
Divide \frac{2c^{2}}{9d} by \frac{6c}{4d^{2}} by multiplying \frac{2c^{2}}{9d} by the reciprocal of \frac{6c}{4d^{2}}.
\frac{4cd}{3\times 9}
Cancel out 2cd in both numerator and denominator.
\frac{4cd}{27}
Multiply 3 and 9 to get 27.