Explanation:
When the internal energy and the work done by a system decreases by the same amount, it implies that the change in the internal energy is equal to the negative of the work done by the system.

First, let's understand the concept of internal energy:
The internal energy of a system is the sum of the kinetic and potential energies of its particles. It represents the total energy stored within the system and is a state function, meaning it depends only on the current state of the system and not on how the system reached that state.

Now, let's analyze the given options:
a) The temperature must decrease:
When the internal energy of a system decreases, it means that the average kinetic energy of its particles decreases. Since temperature is directly proportional to the average kinetic energy of the particles, a decrease in internal energy implies a decrease in temperature. Therefore, option a) is correct.

b) The process must be adiabatic:
An adiabatic process is one in which there is no exchange of heat between the system and its surroundings. In such a process, the change in internal energy is solely due to the work done on or by the system. If the work done by the system is negative (decreasing the internal energy), then the process must be adiabatic. Therefore, option b) is correct.

c) The process must be isothermal:
An isothermal process is one in which the temperature of the system remains constant throughout. In such a process, the change in internal energy is solely due to the exchange of heat between the system and its surroundings. If the work done by the system is negative (decreasing the internal energy), it does not necessarily imply that the process is isothermal. Therefore, option c) is incorrect.

Conclusion:
From the above analysis, it is clear that both options a) and b) are correct. When the internal energy and the work done by a system decreases by the same amount, the temperature must decrease (option a) and the process must be adiabatic (option b). Therefore, the correct answer is option D.