The number of common tangents to the circles x² + y² - 4x - 6y - 12 = 0 and x² + y² + 6x + 18y + 26 = 0 is

For the first circle, C1: x² + y² - 4x - 6y - 12 = 0
Center C1 = (2, 3)
Radius R1 = √(2² + 3² + 12) = √25 = 5
For the second circle, C2: x² + y² + 6x + 18y + 26 = 0
Center C2 = (-3, -9)
Radius R2 = √((-3)² + (-9)² - 26) = √(9 + 81 - 26) = √64 = 8
Distance between centers C1C2 = √((2 - (-3))² + (3 - (-9))²) = √(5² + 12²) = √169 = 13
Since R1 + R2 = 5 + 8 = 13 = C1C2, the circles touch externally.
Therefore, the number of common tangents is 3.