Go straight!

$\text{These lines are tangents.The distance between the to centers is }\\=\sqrt{\{2-(-1)\}^2+\{6-2\}^2}=5=sum~of~radii.\\\text{They touch at a point. }\implies~\text{two internal tangents coinside. }\\\text{Thus only two external and one common= 3 tangents.} ~~~~~~~\huge\color{#D61F06}{3}$

Observe that if a line $l$ has distance $r$ to a point $p$ , then $l$ is tangent to a circle $C$ centered at $p$ with diameter $r$ . (Proving it is easy: if it doesn't touch at all, then it doesn't get within distance $r$ of $p$ ; if it intersects twice, then a point in between the intersections has distance less than $r$ to $p$ .)

Thus draw a circle centered at $(-1,2)$ with radius 2, and another centered at $(2,6)$ with radius 3. Essentially we're asking the number of common tangents to these two circles.

It's well-known that in general, there are four such lines: two external tangents and two internal tangents. However, if the circles touch or intersect each other, the internal tangents might coincide or vanish entirely. In this case, note that the distance between the two centers are $\sqrt{(2 - (-1))^2 + (6 - 2)^2} = \sqrt{25} = 5 = 2+3$ , so the distance between the two centers is exactly the sum of the two radii. So the two circles are in fact tangent to each other, and so the internal tangents coincide. In total, there are only 3 such lines: two external tangents and one internal tangent.