To find the y-intercept of the function \( f(x) = 2x^2 - 5x - 6 \), we need to evaluate \( f(0) \).
Substituting \( x = 0 \) into the function:
\[ f(0) = 2(0)^2 - 5(0) - 6 \] \[ f(0) = 0 - 0 - 6 \] \[ f(0) = -6 \]
The y-intercept occurs when \( x = 0 \), which gives us the point \( (0, -6) \).
Thus, the ordered pair for the y-intercept is:
\[ \boxed{(0, -6)} \]