I see two aspects to this question: (1) whether it is even theoretically possible that the atoms in two water molecules could be rearranged to make two oxygen molecules and two hydrogen molecules, and (2) whether there is a process to break the bonds in water molecules.

To answer (1), we can write out the balanced chemical equation for this process:
2*H₂O -> 2*H₂ + O₂
(Count the atoms of each type in the reactants and products. The balanced equation has the same number of H and same number of O on each side)> This shows that two water molecules have sufficient atoms for two hydrogen molecules, but only one oxygen molecule. (From the wording, I interpreted the question to be asking about oxygen molecules, O₂, rather than monatomic oxygen, O.

Monatomic oxygen does exist, and two water molecules do contain two O's , but monatomic oxygen is highly reactive and will readily bond with other molecules unless there is heavy UV radiation and few other molecules nearby. This essentially means in outer space; monatomic oxygen is not naturally extant in significant amounts near the Earth's surface).

(2) Is essentially asking whether there is a way to put enough energy into the molecule to break the bonds holding the atoms together. There are several methods by which this can be accomplished. One well-known technique is called electrolysis, which involves passing an electric current through water. Here is a simple experiment in which you can split water by using the energy in a battery. Some other methods use light, nuclear radiation, temperature, and photosynthesis. Splitting of water requires large amount of energy though, so it is typically not cost-effective . However, the presence of a catalyst will reduce the energy needed to break the bonds, and an efficient means of producing hydrogen from water would be a key development toward the use of hydrogen as a common fuel, like how we use fossil fuels today.

You can make oxygen and hydrogen from water. But what you suggested is not possible because the number of atoms are not equal. Let me elaborate:

1) Water molecules are made of smaller atoms, with two Hydrogen (H) atoms together with one Oxygen (O) atom forming one water molecule. Or we can simply put one water molecule as H₂O.

2) You can make hydrogen gas and oxygen gas from water. One common way of doing such thing is by electrolyzing water. The key is that water will not decompose or transform into hydrogen gas and oxygen gas automatically, you need to input some extra energy to make this process happening. Another key point is that during the conversion, the total amount of atoms should be conserved. That being said, we can write down the process as:
2 H₂O --> (electrolyze) --> 2 H₂ + O₂.
Here H₂ is one hydrogen gas molecule which has two hydrogen atoms. This is also true to an oxygen gas molecule (O₂).

Therefore, you can make two hydrogen gas molecules and only one oxygen gas molecule from two water molecules.