We can begin by simplifying the first expression:
2a+10b-8-2(4a-6) = 2a+10b-8-8a+12
= -6a+10b+12
Now we need to find the value of c that makes -6a+10b+12 and -6a+20b+c equivalent. In order for them to be equivalent, they must have the same coefficients for a and b. The coefficient for a is already the same (-6), so we just need to make the coefficient for b the same:
10b = 20b
10b - 20b = 0
-10b = 0
b = 0
Now that we have found the value of b, we can substitute it back into either expression to find the value of c:
-6a+10b+12 = -6a+10(0)+12
= -6a+12
-6a+20b+c = -6a+20(0)+c
= -6a+c
Since these expressions are equivalent, their coefficients for a must also be equal:
-6a+12 = -6a+c
Simplifying this equation, we find:
12 = c
Therefore, the value of c that makes the two expressions equivalent is 12.