Answer: I suggest that your friend be available with the extra backpack.
Explanation:
The sentence that has the correct verb mood usage is the third sentence ''I suggest that your friend be available with the extra backpack''.
Verbs usually have to agree with the subject or object in a sentence, it also has to agree with number, plural and singular forms as well.
The first sentence ''Your backpack was being full of clothes'' does not have the correct grammatical subject verb agreement. The sentence can either be written as ''Your backpack was full of clothes'', showing past tense or ''Your backpack is being filled with clothes'' showing present continues tense.
The second sentence ''If we had another backpack, we were going to carry more food'' has 2 clauses that do not agree based on the subject, object verb agreement. The sentence can be written as thus; ''If we had another backpack, we would have carried more food'' or ''We were going to carry more food, if we had another backpack''. Changing the clauses makes the subject and verb agree.
