Endothermic Reactions:
An endothermic reaction is a chemical reaction that absorbs heat from its surroundings. In other words, the products of an endothermic reaction have a higher energy level than the reactants, and energy is required for the reaction to occur.

Explanation:
Let's analyze each given reaction to determine if it is endothermic or not.

Combustion of methane:
The combustion of methane (CH4) is a highly exothermic reaction because it releases a large amount of heat and energy. The reactants (methane and oxygen) have a higher energy level than the products (carbon dioxide and water), resulting in the release of energy. Therefore, the combustion of methane is not an endothermic reaction.

Decomposition of water:
The decomposition of water (H2O) can be represented by the equation: 2H2O -> 2H2 + O2.
This reaction requires energy input to break the bonds between the hydrogen and oxygen atoms in water molecules. The breaking of bonds requires an input of energy, making the decomposition of water an endothermic reaction.

Dehydrogenation of ethane to ethylene:
The dehydrogenation of ethane (C2H6) to ethylene (C2H4) can be represented by the equation: C2H6 -> C2H4 + H2.
This reaction involves the removal of hydrogen atoms from ethane to form ethylene. Breaking the bonds between the carbon and hydrogen atoms in ethane requires energy input, making the dehydrogenation of ethane an endothermic reaction.

Conversion of graphite to diamond:
The conversion of graphite to diamond involves rearranging the carbon atoms in a crystal lattice structure. This process requires energy input to break the bonds in graphite and form new bonds in diamond. Therefore, the conversion of graphite to diamond is an endothermic reaction.

Conclusion:
Based on the analysis, the endothermic reactions among the given options are the decomposition of water, dehydrogenation of ethane to ethylene, and conversion of graphite to diamond. The combustion of methane is an exothermic reaction because it releases heat and energy.