Let's start on Friday's temperature, the problem says that it was -7°F and it was half of the temperature on Thursday, which means on Thursday is was:
-7*2 °F = -14°F.
On Thursday, the temperature was 8°F higher than on Wednesday, then on Wednesday it was:
-14°F - 8°F = -22°F.
On Wednesday the temperature was twice as low as for Tuesday, then on Tuesday it was:
-22°F/2 = -11°F.
On Tuesday, the temperature was 6°F colder than on Monday, then on Monday it was:
-11°F + 6°F = -5°F.
Therefore, the recorded temperature for Monday was -5°F.