Finding the coordinates of a point equidistant from four given points requires finding the center of a sphere that passes through these points. To find the center, we can use the concept of trilateration, which involves intersecting the perpendicular bisectors of the line segments connecting the points.

Step 1: Find the midpoints of the line segments
- The midpoint of the line segment connecting (0,0,0) and (2,0,0) is ((0+2)/2, (0+0)/2, (0+0)/2) = (1, 0, 0).
- The midpoint of the line segment connecting (0,0,0) and (0,3,0) is ((0+0)/2, (0+3)/2, (0+0)/2) = (0, 1.5, 0).
- The midpoint of the line segment connecting (0,0,0) and (0,0,8) is ((0+0)/2, (0+0)/2, (0+8)/2) = (0, 0, 4).

Step 2: Find the slopes of the line segments
- The slope of the line segment connecting (0,0,0) and (2,0,0) is (0-0)/(2-0) = 0.
- The slope of the line segment connecting (0,0,0) and (0,3,0) is (0-0)/(0-3) = 0.
- The slope of the line segment connecting (0,0,0) and (0,0,8) is (0-0)/(0-8) = 0.

Step 3: Find the equations of the perpendicular bisectors
- The equation of the perpendicular bisector of the line segment connecting (0,0,0) and (2,0,0) is x = 1.
- The equation of the perpendicular bisector of the line segment connecting (0,0,0) and (0,3,0) is y = 1.5.
- The equation of the perpendicular bisector of the line segment connecting (0,0,0) and (0,0,8) is z = 4.

Step 4: Find the intersection of the perpendicular bisectors
- The intersection of the equations x = 1 and y = 1.5 is (1, 1.5, 0).
- The intersection of the equations x = 1 and z = 4 is (1, 0, 4).
- The intersection of the equations y = 1.5 and z = 4 is (0, 1.5, 4).

Step 5: Determine the average of the intersection points
- The average of the intersection points is ((1+1+0)/3, (1.5+0+1.5)/3, (0+4+4)/3) = (0.6667, 1, 2.6667).

Therefore, the coordinates of a point equidistant from the given points (0,0,0), (2,0,0), (0,3,0), and (0,0