You need to put subfloor in to cover those holes, making sure it is fully supported. Hardibacker is not structural, only dimensionally stable. With only Hardi-board, if weight is placed over the hole, someone steps in those locations, cracked tile is inevitable.

How would you put subfloor over these holes?

That is a bit difficult to answer without seeing what you have. However, in general, you need to get some sort of support from under the holes, attached to your floor joists. You may need to enlarge the holes to do that. That will give you something to attach new plywood to. You could also look in or reach in to find where your nearest joists are and remove enough flooring to place a piece of plywood such that the ends rest on joists. If the holes are big enough, you may be able to toe-mail cross-pieces to joists through the existing holes, but it'll be tight. Do you, by chance, have access from below? That would certainly make your job easier.

Another thought: If you are essentially starting over with all new flooring, I would forego the hardi-board in favor of an additional layer of plywood (3/4") over the entire floor, followed by Schluter Ditra, then tile.

We do not have access from below. This is a manufactured home. Can I cut down the thickness of the existing sub-floor, out from the hole a distance of 4 inches? Then new sub floor would be supported by what is supporting the existing sublfloor around the hole. Then I could just lay in another piece of subfloor and attach that?

You'll need to cut out to where you have support or large enough to install support. Just make sure you only cut to the midline of the support piece (set the depth on your saw) so both the existing subfloor and the pieces you install will have support from below. Of particular concern with a manufactured home - You need to ensure the floor is strong enough, without deflection or bouncing before installing tile. If your subfloor is not stiff and bends under weight, tile will break since it can't bend.