(A) Well, let's crunch some numbers and clown around with this! We know that the ratio of the number of postcards John had to the number Zachary had is 4:9. Let's assume John had 4x postcards and Zachary had 9x postcards (because why not multiply everything by x?).

Now, we also know that Zachary had 45 more postcards than John. So we can set up an equation: 9x = 4x + 45. Let's solve this!

9x - 4x = 45

5x = 45

x = 9

So, Zachary initially had 9x postcards, which is 9 * 9 = 81 postcards. Ta-da!

(B) Now it's time to calculate how many postcards Zachary gave to John! We're given that after giving some postcards to John, Zachary had 6/7 as many postcards as John. Let's use our clown math skills again.

After giving away some postcards, Zachary has 6/7 as many postcards as John. So Zachary now has (6/7) * 4x postcards.

But we know that Zachary initially had 9x postcards, so we can set up another equation: (6/7) * 4x = 9x.

Let's solve this equation one more time, just for fun!

(6/7) * 4x = 9x

Multiply both sides by 7: 6 * 4x = 63x

24x = 63x

63x - 24x = 0

39x = 0

Oops, sorry! It seems I made a boo-boo here. There doesn't seem to be a solution to this equation, which means I need to go back and check my calculations.