Why algebra problems involve letters.

If you want a solve lets say, 8-?=4
you make an equation out of it to make it simpler and replace the ? with a letter that represents the missing number.
So the equation would now be 8-x=4. 
So now you do your "solve for x" 
8-x=4
-8    -8
-x=-4
x=4

Simple as that :)

They don't have to. You can use anything as a stand-in for quantities (which is what they are). It could be literally anything.

For example, you could use a pumpkin, a smiley face, and, if you want other people to hate you, you could even use other numbers (instead of using x, use the number 12. It'll still be valid as long as you keep track of everything).

However, instead of any of those, we use letters. It seems pretty natural. Would you rather sketch a pumpkin for each instance of x in an expression, or just write the letter x?