For something like $g^{ij} n_i h_{kj}$, how do I know which one should the metric operate on? $n_i$ or $h_{kj}$? The results could be $n^j h_{kj}$ or $n_i h^i_{k}$, which are different.
The question also appears when encountering partial derivatives too, like $g_{ij}\partial_i h^i$