Step 1 :Calculate the left-hand limit at x=6: \(\lim_{x \rightarrow 6^{-}} f(x) = 6^2 + 4(6) + 3 = 63\)
Step 2 :Calculate the right-hand limit at x=6: \(\lim_{x \rightarrow 6^{+}} f(x) = -7(6) + 6 = -36\)
Step 3 :\boxed{\text{Final Answer: } f(x) \text{ has a jump discontinuity at } x=6.}