To find the difference between these two dates, we need to calculate the number of days between them.

First, let's calculate the number of days from June 20th to the end of June (30th):

June 20th to June 30th = 10 days

Next, let's calculate the number of days from the beginning of July (1st) to July 3rd:

July 1st to July 3rd = 2 days

Now, add the two totals together:

10 days (June) + 2 days (July) = 12 days

Therefore, the difference between June 20th and July 3rd is 12 days.