The sentences that use an adverbial clause are:
- So that we would have enough left for tomorrow, we only used half of the vegetables in the salad.
- Javy was named captain of the team despite it being his first year on the team.
The first sentence contains an adverbial clause ("So that we would have enough left for tomorrow") that modifies the verb "used," explaining the purpose of using half of the vegetables. The second sentence has a phrase ("despite it being his first year on the team") that functions similarly to an adverbial clause, indicating a contrast regarding Javy being named captain.
(Note: While "despite it being his first year on the team" can be seen as a prepositional phrase, it can function in a way that relates to adverbial use by indicating circumstances surrounding the action.)
If you want a more strict interpretation and specifically want adverbial clauses (typically introduced by subordinating conjunctions), then only the first sentence is correct.