The correct answer is option 'A': Respiration.

Explanation:
Respiration is the mechanism by which cells obtain energy from glucose and release waste products such as carbon dioxide. Amoebas, being single-celled organisms, also undergo respiration to obtain energy for their cellular activities.

Here's a detailed explanation of the process:

1. Respiration in Amoeba:
- Amoebas are small, unicellular organisms that live in water environments. They require oxygen to carry out respiration and obtain energy.
- Amoebas have a flexible cell membrane that allows them to exchange gases directly with their environment. They do not possess specialized respiratory structures like lungs or gills.
- The process of respiration in amoebas involves the uptake of oxygen (O2) and the release of carbon dioxide (CO2).

2. Uptake of Oxygen (O2):
- Amoebas take in oxygen from their surroundings through a process called diffusion.
- Diffusion is the movement of molecules from an area of higher concentration to an area of lower concentration. Oxygen molecules move from the environment (where they are relatively more concentrated) to the cytoplasm of the amoeba (where they are relatively less concentrated).
- The flexible cell membrane of the amoeba allows the oxygen molecules to pass through and enter the cell.

3. Release of Carbon Dioxide (CO2):
- During the process of respiration, glucose (obtained from food) is broken down in the presence of oxygen to release energy.
- One of the waste products generated during this process is carbon dioxide.
- The carbon dioxide molecules, being at a higher concentration within the amoeba's cytoplasm, move out of the cell through diffusion.
- The carbon dioxide then diffuses from the amoeba's cytoplasm into the surrounding environment, where it is relatively less concentrated.

4. Overall Process:
- The overall process of respiration in amoebas involves the uptake of oxygen and the release of carbon dioxide.
- This process is necessary for the amoebas to obtain energy from glucose and carry out their cellular activities.

In conclusion, the correct mechanism by which amoebas take in oxygen and release carbon dioxide is called respiration (option 'A').