Solution:

To find the value of 8x/2y, we first need to solve the given equation 3x - y = 12 for one variable, either x or y, and then substitute the value into the expression 8x/2y.

Solving the equation 3x - y = 12:

To solve for x, we can rearrange the equation as follows:
3x - y = 12
3x = y + 12
x = (y + 12)/3

Now, we can substitute this value of x into the expression 8x/2y:

8x/2y = 8((y + 12)/3)/(2y)
= (8/2)(y + 12)/(3y)
= 4(y + 12)/(3y)

Simplifying the expression 4(y + 12)/(3y):

To simplify further, we can distribute the numerator:
= (4y + 48)/(3y)

Final Answer:

Therefore, the value of 8x/2y is (4y + 48)/(3y).

Explanation:

To find the value of 8x/2y, we first solved the given equation 3x - y = 12 for x. By rearranging the equation, we isolated x on one side.

Then, we substituted the value of x into the expression 8x/2y. We simplified this expression by canceling out common factors and distributing the numerator.

Finally, we obtained the simplified form of the expression as (4y + 48)/(3y).