Step-by-step Solution:

\[ \text{Consider } n \text{ equally spaced points } 1, 2, \dots, 12 \text{ marked on the circumference of a circle.} \] \[ \text{Number of points on Right side} = (\text{Difference of directly opposite points}) - 1 \] \[ = (12-6)-1 = 5 \] \[ \text{Number of points on Left side} = (\text{Difference of directly opposite points}) - 1 \] \[ = (12-6)-1 = 5 \] \[ \text{Total number of points} = \text{Right side points} + \text{Left side points} + \text{Directly opposite points} \] \[ = 5 + 5 + 2 = 12 \text{ points} \] \[ \text{Calculation:} \] \[ \text{Directly opposite points are } 49 \text{ and } 15. \] \[ \text{Difference of directly opposite points} = 49 - 15 = 34 \] \[ \text{Number of points on Right side} = 34 - 1 = 33 \] \[ \text{Number of points on Left side} = 34 - 1 = 33 \] \[ \text{Total number of points} = 33 + 33 + 2 = 68 \]