This problem involves taking the dot product of two vectors A & B.

The vectors are defined as:
A = 4i+3j+6k
B = 2i-j-4k

The dot product calculation will be performed using IDL.  Put simply,
vector multiplication, dot product, is done by multiplying like indices
directly and then summing the result.  The calculations follow:

IDL> A = [4,3,6]
IDL> B = [2,-1,-4]
IDL> C = total(A*B)
IDL> print, C
     -19.0000