If you wanted to eliminate the y variable by adding the two equations in the following system

what could be your first step?
x − y = 6
−4x − 4y = 10

A. Add the two equations together.
B. Multiply the first equation by −4.
C. Multiply the first equation by 4.
D. Multiply the second equation by −4.

B.
Multiply the first equation by (-4)
-4x + 4y = -24

Then add it to the second equation to eliminate the y variable.
-4x + 4y = -24
-4x -4y = 10
---------------------
-8x = -14
and x = 7/4

to eliminate something by adding, sign must be opposite and multiplier magnitude must be same.
for example:

(17q) + (-17q) = 0

in your case there is -y and -4y. the easiest way is to multiply first equation by -4 (multiply everything, not just y):

then

x - y = 6 ; *(-4)
-4x +4y =-24
the second equation is the same
−4x − 4y = 10


if you add them, y will cancel:

(-4x+4y) + (-4x-4y) = (-24) + (10)
-8x=-14
x=-14/-8=7/4 etc.

B
A would not solve the problem, because it does not get rid of the y.
If you multiply the first equation by -4 that will allow to get rid of the y.
-4(x-y)=6x-4
-4x+4y=-24 Then you add the two equations together.

Do B first, then add the equations together to eliminate y.

I would chose step (B)

-4x + 4y = -24
-4x - 4y = 10

-8x = -14

x = 14/8

A