Step 1: Recall why the day has two dates.
World Migratory Bird Day tracks bird migration in both hemispheres, so it is marked twice a year rather than on one fixed date.
Step 2: Recall the actual dates used.
The observance falls on the second Saturday of May and the second Saturday of October, which this year work out to 9th May and 10th October.
Step 3: Eliminate the other date pairs.
June 30/December 31, January 1/July 1 and April 4/November 4 do not match the officially used pattern.
\[ \boxed{\text{9th May and 10th October}} \]