The equipment ....... delivered tomorrow afternoon.
A) will been B) will be
And I appreciate it if you explain the differences between the two of them.
Did you mean: A) will have been B) will be
In this case the correct answer is B.
"Will have been" is used when the instance occurs before a certain date in the future.
For example: "By 2050, our cars will have been replaced with spaceships."
"Will be" is used when the instance occurs at an exact date in the future.
For example: "Our cars will be replaced with spaceships tomorrow."
The equipment will be delivered tomorrow afternoon.
If you want to use the other answer, you would write:
The equipment will have been delivered by tomorrow afternoon.