To find the value of this expression, we need to use the trigonometric identity:

sin(a) cos(b) + sin(c) sin(d) = (1/2) * (sin(a+b) + sin(a-b))

So, the expression simplifies to:

sin(126+216) + sin(126-216) = sin(342) + sin(-90)

We know that sin(-x) = -sin(x), so sin(-90) = -sin(90) = -1

Therefore, the expression simplifies to sin(342) - 1.

Now, we know that sin(342) = sin(360-18) = sin(18), so the final answer is sin(18) - 1.

Therefore, sin(126) cos(216) + sin(144) sin(324) is equivalent to sin(18) - 1.