Question 12275
It's a little riddle, that's all. y is a symbol for a number. It's just a number. Now the equation (two things equal) says 
3y + 4 is equal to 5y +6.
That means: there is a number y that fits the following description:
If you multiply y by 3 and add 4 you get a resulting number.
If you multiply y by 5 and add 6 you get a resulting number. 
What does y have to be so that those two resulting numbers are equal?
Algebra is the study of such questions, and has developed some "rules" that allow you to find the answer by manipulating the algebraic expressions. (An algebraic express is an arithmetic experssion like 2 + 3 times 4, but with one or more of the numbers replaced by a name. Usually in simple cases the name is a single letter, like "y.")
For example: a basic rule is that if two numbers are equal (6=6) and you add a number to one of them, you only keep them equal if you add the same number to the other one. This is usually stated as "Equals added to equals are equal." (Namely, 6=6 added to 3=3 gives 9=9.) Cute, no? So if you add 3 to one of the 6's, you have to add 3 to the other one, giving 9=9.
Now we don't have 6=6; we have 3y+4 = 5y+6. But each side is just a number!
Let's say we add something to the left expression (3y+4). But what? Well, how about adding {{{-3y}}} to it? {{{-3y+3y+4 = 4}}}. But 4 no longer equals 5y+6. We have to add -3y to the other expression, too. -3y+5y+6 = 2y+6. (If you don't believe this, just remember what 5y means: y+y+y+y+y. And -3y means -y-y-y. So you end up with 2y.
Now we still have an equation, namely, 4 = 2y+6.
At this point we can add -6 to both sides! This gives -2 = 2y.
What is true about adding the same number to both sides is also true if we multiply both sides by the same number (since multiplying is just adding over and over). So let's multiply both sides by 1/2.
We get -1 = y. Egad, the "answer."
Naturally, the numbers you pick to add to both sides, or multiply by both sides, are selected with skill, intelligence, and guesswork so as to get the "answer." But practice will show you how to pick good numbers to work with.
Anyway, I hope this helps.