To find the gradient of the curve, we need to differentiate \(y = \frac{2}{\sqrt{5x - 6}}\) with respect to \(x\).

First, rewrite the equation as \(y = 2(5x - 6)^{-\frac{1}{2}}\).

Using the chain rule, the derivative \(\frac{dy}{dx}\) is:

\(\frac{dy}{dx} = 2 \times -\frac{1}{2} \times (5x - 6)^{-\frac{3}{2}} \times 5\).

Simplifying, \(\frac{dy}{dx} = -\frac{5}{(5x - 6)^{\frac{3}{2}}}\).

Substitute \(x = 2\) into the derivative:

\(\frac{dy}{dx} = -\frac{5}{(5(2) - 6)^{\frac{3}{2}}} = -\frac{5}{(10 - 6)^{\frac{3}{2}}} = -\frac{5}{4^{\frac{3}{2}}}\).

Since \(4^{\frac{3}{2}} = 8\), the gradient is \(-\frac{5}{8}\).