The simplest way to think of this is a ratio. In the original 7 cards used for demonstration, 4 are blue. You can write it like this:
Since there are 84 total cards, and you need to find how many total blue cards there are, you can compare the total of the sample to the complete total, and then solve for an x value of total blue cards.
= 
You can solve using cross multiplication. 84*4=336. 7*x=336.
x=48
Since there are 84 total cards, and you need to find how many total blue cards there are, you can compare the total of the sample to the complete total, and then solve for an x value of total blue cards.
You can solve using cross multiplication. 84*4=336. 7*x=336.
x=48