Hint 1: The Scale
Pick up the scale's weights, and add just enough weight so that the arrow points to green.
Add the largest weight and the smallest weight, and the scale will balance to green. There will be a click, a ding, and the drawer will open. Pick up the scroll from the drawer, and read the poem.
Hint 2: The Clock
"The First Hides on a Clock." Notice anything on the clock face? A math puzzle, perhaps?
"12 Divided by 6," so the first number is 2.
Hint 3: The Sky
"The second in the sky." Is there anything flying? You might want to check da Vinci's Air Screw, the model helicopter that's suspended in the corner.
"8 - 2," so the second number is 6.
Hint 4: The Drawer
"The third sits in a drawer." Next to one of the bookcases is a chest of drawers. Three of the drawers give you hints, but the second drawer has the puzzle.
4 balls, a plus sign, and 5 balls. That's 9 -- the third number!
Hint 5: Pi
"The last is marked by Pi." Do you see anything marked by the symbol π? Perhaps on the pinboard?
"π is 3.14, but what is ( 3 x 1 ) + 4?" Yep... the last number is 7.
Hint 6: The Combination
To escape this room, set the exit door's combination lock to 2697.