Here's the picture you started out with:
The first question was to determine how many units (arrows) of energy
the atmosphere needs to emit to be in energy balance. The
atmosphere is absorbing 3 units (highlighted below): 1 from sunlight
and 2 are IR radiation emitted by the earth. To be in balance the
atmosphere must also emit 3 units.
How many of the units would need to be sent upward and into
space. The intent was for you to determine how many of the 3
units emitted by the atmosphere would need to be sent upward and into
space (the original wording might not have made that clear). The
atmosphere would need to send 1 unit upward into space. This is
the blue arrow (highlighted) in the figure below.
2 units (sunlight) are coming in and arriving at the top of the
atmosphere and 2 units (one from the ground, the other from the
atmosphere) are going out. That part of the picture is in
balance. The 2 remaining units emitted by the atmosphere must
travel downward (again the wording in the original question might have
been misleading). They are shown below.
Now the ground (which is absorbing 3 units and emitting 3 units) is in
balance.
However you interpreted the original questions your final drawing
should have looked like the one above.