Protection does four things (DEBT):
prevents DAMAGE from things with the stated quality
can't be ENCHANTED or EQUIPPED by the things with the stated quality
can't be BLOCKED by things with the stated quality
can't be TARGETED by things with the stated quality
Sinkhole falls in the last one in this case. So, since Sinkhole's target will be illegal upon resolution, the spell will be countered on resolution and do nothing.
For clarity, Enchantments on a permanent that now have Protection from the color of that enchantment gets destroyed (relevent if a deathlace is about! )