I took a somewhat different approach. I figured that the user would
enter "Year" only A1, and from there want to know all of his 2nd and
4th Wednesdays in a list.

So the first thing is to find which day (between 8 and 14) is the 2nd
Wednesday of January of Year value stored in A1.

After that, a single formula figures out each other date in the list.

The first formula I used (at cell E1) is:
=DATE( A1, 1, 8) + 4 - WEEKDAY( DATE( A1, 1, 8)) + IF( WEEKDAY( DATE(
A1, 1, 1)) 4, 7, 0)
(The 4 value represents the day of the week we want, Wednesday.
Substituting other values from 1 to 7 would give the other days of the
week, and would re-figure the remaining days in the list to be same day
of week.)

The next formula, used to generate the rest of the list, is:
=IF( DAY( E1 + 14) = 8, E1 + 14, E1 + 21)

Copy that one down the next 23 rows and you have the entire list of
dates.

Chris