Endothermic Reactions:
An endothermic reaction is a chemical reaction that requires the absorption of energy from its surroundings in the form of heat. In these reactions, the products have a higher energy content than the reactants, meaning that energy is being stored in the products. Let's analyze each of the given options to determine which one(s) are endothermic reactions.

Combustion of methane (CH4):
The combustion of methane is an exothermic reaction. It releases energy in the form of heat and light. Methane reacts with oxygen to produce carbon dioxide and water vapor, and this reaction is highly exothermic. Therefore, option 'a' is not an endothermic reaction.

Decomposition of water (H2O):
The decomposition of water is an endothermic reaction. Water can be decomposed into its constituent elements, hydrogen and oxygen, through the application of energy. This reaction requires the absorption of heat to break the bonds between hydrogen and oxygen atoms. Therefore, option 'b' is an endothermic reaction.

Dehydrogenation of ethane (C2H6) to ethylene (C2H4):
The dehydrogenation of ethane to ethylene is an endothermic reaction. In this reaction, ethane loses hydrogen atoms to form ethylene. Breaking the C-H bonds in ethane requires the absorption of energy. Therefore, option 'c' is an endothermic reaction.

Conversion of graphite to diamond:
The conversion of graphite to diamond is an endothermic reaction. Graphite and diamond are both forms of carbon, but they have different crystal structures. The conversion of graphite to diamond involves rearranging the carbon atoms into a different lattice structure. This rearrangement requires the absorption of energy. Therefore, option 'd' is an endothermic reaction.

Conclusion:
Based on the analysis, options 'b', 'c', and 'd' are endothermic reactions. The decomposition of water, dehydrogenation of ethane to ethylene, and conversion of graphite to diamond all require the absorption of energy from the surroundings.