To integrate \(\int \left( 4x + \frac{6}{x^2} \right) \, dx\), we integrate each term separately.

1. Integrate \(4x\):

\(\int 4x \, dx = 4 \cdot \frac{x^2}{2} = 2x^2\).

2. Integrate \(\frac{6}{x^2}\):

Rewrite as \(6x^{-2}\).

\(\int 6x^{-2} \, dx = 6 \cdot \frac{x^{-1}}{-1} = -6x^{-1}\).

Combine the results:

\(2x^2 - 6x^{-1} + c\), where \(c\) is the constant of integration.