Step 1: Break down 'transient': the prefix 'trans-' means across or through, and the root relates to 'going', so a transient thing is one that is passing through or lasting only briefly.
Step 2: An antonym must describe something that does not pass through quickly but instead stays. Check 'temporary', 'fleeting', and 'brief': all three describe things that last only a short time, meaning they sit on the same side of the meaning spectrum as 'transient', not the opposite side.
Step 3: 'Permanent' describes something that lasts indefinitely without passing away, placing it at the opposite end of the duration spectrum from transient.
Correct option: (1) Permanent.