A. "What it looks like"
This is a pointer indicating equivalence or similarity between this what and another what (things you can look at/see).
B. "How it looks"
This is a pointer indicating equivalence or similarity between this what and another what (things you can look at/see).
C. "How it looks like"
This is a pointer indicating similarity between, as seeing in a similar way or manner.
The erratic history of C's usage would tend to reflect what our care for precision of expression looks like.
The erratic history of C's usage would tend to reflect how our care for precision of expression looks.
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I submit C is an error. Stop it.
PS And now (17.07.16) I find this, to my dismay: 'Pokémon GO' Unofficial Demo Shows How It Could Look Like On Microsoft HoloLens
PS And now (17.07.16) I find this, to my dismay: 'Pokémon GO' Unofficial Demo Shows How It Could Look Like On Microsoft HoloLens