How do you find a=b+2c given b=<6,3> and c=<-4,8>?
I'm interpreting what you wrote as the specification of two vectors.
You need a scalar multiple of vector c, for this just multiply each component by 2:
2c = <-8,16>
Then the vector sum is found by simply adding the respective components...
b + 2c = <6,3> + <-8,16> = <-2,19>