Why does this current source absorb but not deliver power?
VCCS absorbs 192 W. This doesn't make sense. The current flows in the
  same direction as VCCS (0.8 Vab). It should deliver and not absorb
  power.


But it does make sense since the source is absorbing power.  According to the solution, the voltage across the VCCS is 12V with the top terminal more positive.

Since the 16A current enters the more positive terminal of the VCCS, power is delivered to the source.  See the passive sign convention.

Note that, for the 10A source, the 10A current exits the more positive terminal so that source is delivering power.

Also, note that, for the 20V source, the 6A current exits the more positive terminal so that source is delivering power.




  my main point of confusion is still why is VCSS + on top - on bottom
  and why is 10A - on top and + on bottom


The 10A source is + on top which is why it's delivering power.  Look at the solution:



(1) due to the 20V voltage source on the left, the top circuit node is 20V more positive than the bottom node

(2) the center node between the two controlled sources must by 8V more positive than the bottom node (the CCVS is configured as a 1/2 ohm resistor and \$16A \cdot 0.5 \Omega = 8V\$)

(3) thus, by KVL, the top node must be 12V more positive than the center node.