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\begin{aligned} \lim\limits_{x \rightarrow-3}(4 x+2) &=\lim\limits_{x \rightarrow-3} 4 x+\lim\limits_{x \rightarrow-3} 2 & & \text { Apply the sum law. } \\ &=4 \cdot \lim\limits_{x \rightarrow-3} x+\lim\limits_{x \rightarrow-3} 2 & & \text { Apply the constant multiple law. } \\ &=4 \cdot(-3)+2=-10 . & & \text { Apply the basic limit results and simplify. } \end{aligned}