Select the sentence from the given options that has used the correct…

The correct answer is Option (1) → The boss sees everything in black and white.

To see something in black and white means to judge it in simple, absolute terms, as either fully right or fully wrong, with no middle ground. The boss judges every matter in this clear-cut way, so the colour idiom is used correctly.
Example: Life is not always black and white; some problems have no single right answer.

Why the Other Options are Incorrect?

Option 2: Her mistakes left her pink faced. — Incorrect. There is no idiom "pink faced". The idiom for being embarrassed or ashamed is red-faced.
Corrected: Her mistakes left her red-faced.
Example: He was red-faced when the teacher read out his wrong answer.

Option 3: We saw her turning yellow when her competitor walked the ramp with aplomb. — Incorrect. Yellow stands for cowardice, not jealousy. A person who feels envy at a rival's success is green with envy.
Corrected: We saw her turning green with envy when her competitor walked the ramp with aplomb.
Example: Her classmates were green with envy when she won the scholarship.

Option 4: My new car is like a gray elephant. — Incorrect. The idiom is a white elephant, meaning a costly possession that is a burden to keep and of little use; "gray elephant" is not an idiom. It comes from the story that the kings of Siam (Thailand) gave a sacred white elephant to a courtier they disliked, knowing that its upkeep would ruin him.
Corrected: My new car is like a white elephant.
Example: The huge stadium became a white elephant after the games were over.