Concept:The correct word must show contrast and fit grammatically before the noun phrase “the difficulties involved”.
Explanation:The blank is followed by the noun phrase “the difficulties involved”.
A preposition such as “despite” can directly precede a noun phrase.
“Despite” means “in spite of” or “without being affected by”.
This gives the meaning: the road was completed on schedule even though difficulties existed.
“Although” is a conjunction and needs a full clause after it, like “although the difficulties were many”.
“However” is an adverb used with a semicolon or as a separate sentence, not after a comma in this way.
“Besides” means “in addition to” and does not express contrast.
Therefore, “despite” is both grammatically correct and logically suitable.
Answer:B. despite