opps! do not know if my follow up question made it to this site. We started removing sheet vinyl and discovered it was put down using some sort of mastic as we can see the "thinset" tracks. We have 1/2" subfloor. Can we lay 1/4" flooring over the vinyl then use the 1/4" hardibacker. We are using 20x20 porcelain tiles.

Prior to tiling:
is the floor structure strong enough, rigid enough?
Based on your questions, I believe you don't know anything about this.
If you are willing to live with hairline cracks in your tiles, keep reading.

Tiling:
one may lay tile onto linoleum. It has been done.
one may lay a membrane onto linoleum like Ditra, or a CBU like hardibacker.

There is a difference between vinyl and lino.
Based on your two posts I believe you don't know.

Hope this helps.

"We have 1/2" subfloor."

The sub-floor is to thin for tile.

Can you feel it flex as you walk?

Even in 16 inch joist centers the tile will not last long.

The grout will fracture quickly for larger tiles, then the tiles will start to crack.

For small mosaic tiles the tiles may hold together, but the grout will come out quickly.