Understanding how to solve for algebra with the properties

I don't exactly understand what you are asking but I can help you with the problem. 

You start with this:       35 - 4y = y

All I did here was add 4y to both sides because I eventually want it to cancel off of one side. We are left with:        35 - 4y + 4y = y + 4y           

Now you combine like terms. The like terms on the left are -4y and 4y. adding these gives you zero so it is no longer there. The like terms on the right and y and 4y. Adding these gives you 5y. The y only has one term on its side now so we are almost done.     35 = 5y

From here you can now divide both sides by 5 giving us:         5 = y

Basically, in Algebra when you are asked to solve an equation, you can do any basic property (+, -, x, /), as long as you do it to both sides. For example, you can subtract a 2 from both sides of this equation:

y + 2 = 6             This gives you y = 4

If you are ever unsure about an answer you get, you can always plug it back into the equation, and the equation should be a true statement if you did it right.