For vector arithmetic, vector addition (adding two vectors) and scalar multiplication (multiplying a vector by a scalar) is "component-wise". So when adding two vectors you add each component in the first vector to the corresponding one in the second to get the resulting vector. In scalar multiplication you multiply each vector component by the scalar and that gives the resulting vector.
So if u = <3,-2> and v = <-1,4>,
3u = <3*3,-2*3> = <9,-6>
2v = <-1*2,4*2> = <-2,8>
3u + 2v = <9,-6> + <-2,8> = <9+(-2),-6+8> = <7,2>