Italicized clause: that he run the mile in less than four minutes.
Answer:
Appositive
Step-by-step explanation:
The noun clause “that he run the mile in less than four minutes” is an appositive because it gives us further information about another noun placed right beside it: “goal.” Besides, it is a nonrestrictive appositive because its information is not essential to the meaning of the sentence (without it, the sentence would still make sense).