Half the original number of trash cans in Veteran's Park is 24/2=<<24/2=12>>12 trash cans.
Thus Central Park originally had 8 more than half the number of trash cans as what was originally in Veteran's Park, or 12+8=<<8+12=20>>20 trash cans.
Half of the trash cans from Central Park is 20/2=<<20/2=10>>10 trash cans.
After the addition of the 10 new cans, there are now 24+10=<<24+10=34>>34 trash cans in Veteran's Park.
#### 34