If you are given a calendar for July you can see what day of the week July 25th is.
So add up the number of days in each month you need to move on by:
31 for July, 31 for August, 30 for September, 31 for October, 30 for November - total 153.
Divide by 7 to get weeks -> 21 remainder 6.
So 25th December will be the weekday before 25th July.
Remember to use the number of days starting from the first month (e.g. July), but not the last (e.g. December). In this case it is the same but it isn't always.
There is a formula (google "Zeller's Rule") but I'd suggest not even trying to memorise it. Adding up the month lengths and dividing by 7 is much simple and more appropriate for the type of question you have described!
A similar but slightly different way is to just add up the additional days above 28 that each month has (because 28 is an exact multiple of 7).
So using the same example that's - 3 for July, 3 for August, 2 for September, 3 for October, 2 for November - total 13.
That's 1 less than 14 (2 whole weeks) so any particular date in December will be 1 day of the week before the equivalent day in July for the same date.
Its essentially the same theory but perhaps slightly easier to do in your head because you only need to add up 3, 3, 2 etc rather than 31, 31, 30 etc, and also the final total of additional days, 13, is easier to compare against an exact mulitiple of 7 than 153 is.