How can I removes stains from a candle (probably the red parafin) left
on the counter of a solid sink/countertop. It is not marble but
"marble like".  I do not recall the exact name of the sbustance from
which it is made.  Thank you.

Is it another natural stone or is it perhap duPont's "Corian"?

If it is the latter, try a non-metal scouring pad (one used to be
supplied with Corian fixtures).  Otherwise, the instructions were to
use fine sandpaper carefully.

Try making a paste of baking soda and warm water.  Lay a hot, wet
cloth on the stain for a few seconds then remove and rub the paste
into the stain with a toothbrush.  Leave the paste on (thick!) for a
couple of hours then scrub again with toothbrush and hot water and
rinse clean. If the stain is still there, wet a paper towel with
alcohol and leave on the stain for a few minutes and try another quick
scrub with the paste.