1. **State the problem:** We need to find the slope of the tangent line to the function $f(x) = 4\sin x + 2$ at the point $a = (\pi, 2)$. 2. **Recall the formula:** The slope of the tangent line to a function at a point is given by the derivative of the function evaluated at that point. So we need to find $f'(x)$ and then calculate $f'(\pi)$. 3. **Find the derivative:** The derivative of $f(x) = 4\sin x + 2$ is $$f'(x) = 4\cos x + 0 = 4\cos x.$$ 4. **Evaluate the derivative at $x = \pi$:** $$f'(\pi) = 4\cos \pi = 4 \times (-1) = -4.$$ 5. **Interpretation:** The slope of the tangent line to the curve at the point $(\pi, 2)$ is $-4$. This means the tangent line is decreasing at that point with a slope of $-4$.