Note that f is continuous on (−∞, 6) and (6, ∞). For the function to be continuous on (−∞, ∞), we need to ensure that as x approaches 6, the left and right limits match.

Question

First we find the left limit.
lim
x→6−
f(x) =
lim
x→6−
(cx2 + 3x)

Answer 1

evidently
f(x) = 6 - c x^2 - 3 x
left of x = 6

but you do not say what your function is to the right of 6

anyway the idea is to find c so that the functions are the same at x = 6