To differentiate \(4x + \frac{6}{x^2}\), we first rewrite \(\frac{6}{x^2}\) as \(6x^{-2}\).

The derivative of \(4x\) with respect to \(x\) is 4.

The derivative of \(6x^{-2}\) with respect to \(x\) is found using the power rule: \(\frac{d}{dx}[x^n] = nx^{n-1}\).

Thus, \(\frac{d}{dx}[6x^{-2}] = 6(-2)x^{-3} = -12x^{-3}\).

Combining these, the derivative is \(4 - 12x^{-3}\).