The equations at the beginning are wrongly stated. They should be:
2x/5+4y/7=8
3x/8+5y/6=12
(The second variable doesn’t need to be y—it can be any variable other than x.)
This is because in a system of equations which can be solved uniquely there must be as many unknowns as there are equations. If x is the only unknown (as presented in the given two equations) only one equation would be needed to find x. Each of the given equations would give a different value for x when solved, so one or both equations would be false. With two unknowns, x and y, the system can be solved uniquely (one value for x and one for y).
So using the revised equations above, we multiply the first by 35 (the LCD of 5 and 7):
14x+20y=280,
and the second by 24 (LCD of 8 and 6):
9x+20y=288. That is, 20y=288-9x, which can be substituted into the other equation:
14x+288-9x=280 which is one of your answer options.
Alternatively, we could have used 20y=280-14x and then substituted in the other equation:
9x+280-14x=288, another of your answer options.
Either substitution is correct. The idea in solving systems of equations is to reduce the system eventually to a single equation with a single unknown. Then solve for the unknown, and use the value to find the remaining unknown(s). There are always a number of different ways of solving simultaneous equations, and all are equally valid, although some methods may be faster than others.