System

It is always nice to show some work alongside an an answer. :))

That way, people can learn and share ideas. 

y = 2x^2 + kx + 6

y = -x - 8

-x - 8 =  2x^2 + kx + 6

0 = 2x^2 + (k+1)x + 14

There is one solution when the discriminant is 0.

(k+1)^2 - 4(2)(14) = 0

(k+1)^2 = 112

k+1 = +/- 4sqrt(7)

k = -1 +/- 4sqrt(7)

I did not seem to get 16. 

=^._.^=

k has to be negative, so the answer is \(\color{brown}\boxed{1 - 4 \sqrt7}\)

Here is the graph: https://www.desmos.com/calculator/fwa8nyw6it

It has to be negative, so, unfortunately, you're not right. But, good try tho!

thx