The given sentence means that the subject could barely see the mountain through the fog. In the answer, the subject(He) and the object(mountain) remains the same. Thus, the rest of the phrase must mean 'barely able to see'.
Option A is incorrect. In the given sentence, 'make off' means 'leave hurriedly'. Thus, it indicates that the subject left hurriedly with the mountain's shape. This does not make any sense and thus, it is incorrect.
Option B is correct. In the given sentence, 'make out' means 'detect with difficulty'. This meaning is the closest to 'barely able to see' among the given options. Thus, it indicates the required meaning and is the correct answer.
Option C is incorrect. Here 'make over' means 'use again in altered form'. Thus, it indicates that the subject was able to use the mountain's shape in an altered form. This does not make any sense and is incorrect.
Option D is incorrect. Here 'make up' means 'form'. It indicates that the subject formed the mountain's shape which is senseless. Thus, it is incorrect.