To construct triangle ABC with sides 6, 8, and 9 and bisect all three angles, you can follow these steps:

1. Draw a line segment AB with a length of 8 units. This will represent one side of the triangle.
2. From point A, draw an arc with a radius of 6 units (length of side BC). From point B, draw another arc with a radius of 9 units (length of side AC). The two arcs should intersect at a point, which we’ll call point C.
3. Draw line segments AC and BC to complete the triangle. Now you have triangle ABC with sides 6, 8, and 9 units.
4. To bisect the angles of triangle ABC, find the midpoints of each side. To do this, draw a perpendicular bisector for each side.
5. To bisect angle A, find the midpoint of side BC (let’s call it D). Draw a line from point D to point A. This line will bisect angle A.
6. To bisect angle B, find the midpoint of side AC (let’s call it E). Draw a line from point E to point B. This line will bisect angle B.
7. To bisect angle C, find the midpoint of side AB (let’s call it F). Draw a line from point F to point C. This line will bisect angle C.
8. The three bisectors should intersect at a point within the triangle. Let’s call this point O. Point O is the incenter of triangle ABC, which is the point where all three angle bisectors meet.

You now have triangle ABC with sides 6, 8, and 9, and all three angles bisected, with the bisectors meeting at point O (the incenter).