Question

evaluate the dot product of (2 4) and (1 -2)

Answer 1

That would be 2*1 + 4*-2 = 2 - 8 = -6 Answer

Answer 2

I'd suggest writing this as

<2, 4> dot <1, -2>.  Another name for this is "scalar product."

Rule:  <a,b> dot <c,d> = ac + bd

Thus, 

<2, 4> dot <1, -2> comes out to (2)(1) + (4)(-2) = -6 (which is a scalar).