Think of x as a paper cup containing a number. You can use x in arithmetic calculations just like any other number, you just don't know its value.
That's where equations come in. The number to the left of the = sign is equal to the number on the right of the = sign.
As long as you do the same arithmetic operation to both sides of an equation, you get another equation.
6-x=15 is an equation with the number 6-x on the left and 15 on the right.
Let's add the number x to both sides of the equation:
6-x+x=15+x
Notice that -x+x is zero because a number subtracted from itself is zero; so:
6 = 15+x
Now let's subtract 15 from both sides of the equation:
6-15 = 15+x-15 = 15-15+x = x
I.e., x = 6-15 =-9
(A number line has a point labeled zero (0) and points at equal intervals extending in both directions away from 0. For a horizontal number line the points to the right are labeled with the positive integers in sequence, and the points to the left are labeled with the negative integers in sequence. To find 6-15 start at the +6 point and walk 15 points in the negative/left direction and you will arrive at the -9 point.)