The guiding principle for determining valency is the Octet Rule. This states that all atoms will prefer to have a full valency shell. In practice, this doesn't always mean there must be eight electrons, and with only the molecular formula to work with, we have to incorporate a little of our own background knowledge of oxygen and hydrogen. Practically speaking, it's much more straightforward to use the periodic table and know what the ground state valency for each element is before you start.
We know there are two hydrogens bound to the oxygen atom, which means there must be at least a single bond in each case (we would need more than the molecular formula if there were double or triple bonds). Each single bond provides one extra electron, so we know this provides two electrons to the oxygen in total. If these two electrons satisfy the Octet Rule, then the oxygen is happy and its valency must be 6. Likewise, the hydrogens must have a valency of one because we know there's one bond and they only have one electron to provide. Another key piece of information is that the entire molecule is shown with a neutral charge, which means all the atoms are either in their ground states or there is an equal number of protons and electrons in the molecule.
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