Question

the following is a redox reaction. show which element(s) are oxidized and reduced. include how many total electrons are gained or lost by each element. 3HNO---->HNO3+H2O+2NO

Answer 1

I am not sure if you have a typo, but for the reaction to be balanced, that should be Nitrous Acid (HNO2) in the reactant side:
3HNO2 -> HNO3 + H2O + 2NO
Note that all the species here are neutral (zero charge). Thus the sum of the individual charges of each element involved should be zero.
H usually has a +1 charge
O usually has a -2 charge
Now we'll check the charge of N in the species containing N (let x = charge of N):
HNO2 :
1 + x + 2(-2) = 0
1 + x - 4 = 0
x = +3

HNO3 :
1 + x + 3(-2) = 0
1 + x - 6 = 0
x = +5

NO :
x + (-2) = 0
x = +2

Therefore, N is both oxidized and reduced. The original is +3 (HNO2), it's oxidized state is +5 (HNO3) and reduced state is +2 (NO). The number of e- lost is 2 (from +3 to +5), and e- gained is 1 (from +3 to +2).

Hope this helps :D