When hydrogen combines with oxygen to produce water, this is what kind of reaction?

A) double-displacement
B) endothermic
C) synthesis
D) combustion

The answer to your question is the letter C) Synthesis.

Explanation:

Data

H₂  and O₂ produces water

Balanced chemical reaction

                                2H₂  +  O₂   ⇒   2H₂O

Definition of the kinds of reactions

A) double-displacement   is a reaction where the cations and anions of the reactants are interchanged.

B) endothermic  is the chemical reaction that needs a supply of energy to proceed.

C) synthesis  is the chemical reaction where two reactants combine to form only a product.

D) combustion is the chemical reaction where a compound with carbon reacts with oxygen to form carbon dioxide and water.

Conclusion

From the information given we conclude that the reaction between hydrogen and oxygen is a synthesis reaction.