How is ATP hydrolysis reaction a coupling process?

Hint: Adenosine triphosphate (ATP), an energy-carrying molecule found in all living things' cells. ATP absorbs chemical energy from the breakdown of food molecules and uses it to power other cellular processes.

Complete answer:
ATP hydrolysis may be a catabolic reaction process that releases energy that has been stored within the high-energy phosphoanhydride bonds in ATP (ATP) by splitting these bonds, for instance, in muscles, by producing the shape of energy. Cells typically employ a strategy known as reaction coupling, in which an energetically favourable reaction (such as ATP hydrolysis) is directly linked with an energetically unfavourable (endergonic) reaction. The linking is frequently accomplished via a shared intermediate, which means that a product of one reaction is "picked up" and used as a reactant in the second reaction.

When ATP is used in a reaction, the shared intermediate is frequently a phosphorylated molecule (a molecule to which one of the phosphate groups of ATP has been attached). Consider the formation of sucrose, or table sugar, from glucose and fructose as an example of how this works.

The hydrolysis of ATP is highly exergonic.
\[ATP+{{H}_{2}}O\to ADP+Pi;~\Delta G=-30.5\text{ }kJ/mol\]

As this process is highly favourable, it occurs spontaneously. Many enzymes can use the free energy released by ATP hydrolysis to drive an unfavourable thermodynamic reaction. This is known as ATP coupling. For example, the conversion of glucose to glucose-6-phosphate is thermodynamically unfavorable. \[glucose+{{P}_{i}}\to glucose-6-P+{{H}_{2}}O;~\Delta G=+14.3\text{ }kJ/mol\]

The enzyme hexokinase connects these two reactions, allowing the energy released by the hydrolysis of ATP can be used to boost the synthesis of glucose-6-phosphate
The reactions are:
\[\begin{align}
  & \underline{\begin{align}
  & glucose+{{P}_{i}}\to glucose-6-P+{{H}_{2}}O;~\Delta G=+14.3\text{ }kJ/mol \\
 & ATP+{{H}_{2}}O\to ADP+{{P}_{i}};~\Delta G=-30.5\text{ }kJ/mol \\
\end{align}} \\
 & glucose+ATP\xrightarrow{hexokinase}glucose-6-P+ADP;~\Delta G=-16.2\text{ }kJ/mol \\
\end{align}\]

The coupled reaction has negative free energy, so the process is thermodynamically favourable.

Note: The hydrolysis of the phosphate groups in ATP is especially exergonic because the resulting inorganic phosphate molecular ion is greatly stabilized by multiple resonance structures, resulting in lower energy products (ADP and Pi) than the reactant (ATP). The high negative charge density associated with ATP's three adjacent phosphate units also destabilizes the molecule, causing it to be more unstable energy.