Suppose the solution x=6 increases to x=9 and the left side of the equation stays the same. How would the right side need to change if the solution is now x=9

Given that solution for some equation is x=6

Now they want to change x=6 into x=9.

Notice that all equations contans equal sign (=) because both side values are always same.

So if by any chance you want to change value of one side then you must change value on other side too

like we see that 6 changed to 9 by adding 3 on right side then we must add 3 on the left side too

so we get:

x=6

x+3=6+3

x+3=9

Now question says that the left side of the equation stays the same. That is possible only if we move + 3 to the right side from the left side so we can write;

x=9-3