Answer: 4 cm
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The base of the carton is 5*8 = 40 square cm. The height of the milk is 12 cm, so the milk takes up 40*12 = 480 cubic cm of volume. Imagine a rectangular block with dimensions 5, 8 and 12. The volume would be 480.
The carton is placed on its side. Specifically the orange side is flat on the table (assume the table is level). This orange face has area 8*15 = 120 square cm. It multiplies with some height h, which is the height of the milk after moving the carton, to get the volume of the milk inside.
The volume of the milk is 120h and it must be equal to 480 since the amount of milk has not changed as we moved the carton (assume there are no leaks)
So,
120h = 480
120h/120 = 480/120
h = 4
The height of the milk after moving the carton is 4 cm