What would you like to understand?

A covariant 2-tensor field is linear over the ring of smooth functions. If $X, Y$ are vector fields and $f, h$ are smooth functions, then $g(fX, hY) = f h g(X,Y)$.

Conditions: $g$ is a covariant 2-tensor field.; $X, Y$ are vector fields.; $f, h$ are smooth functions.

A covariant 2-tensor field is linear over the ring of smooth functions. If $X, Y$ are vector fields and $f, h$ are smooth functions, then $g(fX, hY) = f h g(X,Y)$.

Conditions: $g$ is a covariant 2-tensor field.; $X, Y$ are vector fields.; $f, h$ are smooth functions.