you might think Hecarim is a cute little pony ? well he is :3 but he'll kick your aws in solo mister blue buff

start with what you can see above

wait for

ancient golem to spawn while taking care no ennemy is invading start with your Spirit of Dread


you're going to want to Smite really early when Spirit of Dread is still active so that you get a bit more heal in

you might want to use 1 or 2

Health Potion to maintaint high health

once you killed that

Ancient Golem kill those small ones, you'll lvl up and you will want to get Rampage so that you deal that extra damage
then you are going to want to do

the

wolves

wraith

the

lizard elder

before you engage the

lizard elder make sure your Smite is up , you also might want to finish your Health Potion and now that you have your Red buff you will easilly do the golem

Now you nearly emptied your side of the jungle so you should recall you probably have just enough to buy Spirit Stone or Madred's Razors make your choice ;)

Finish of the remaining monsters and now your side of the jungle is pretty empty

if the ennemy team as a

jungler

you probably are more advance than he is
get a vison ward or whatever and try catching him low heath against blue or red

now you killed him it's time to invade the ennemy jungle and kill every monster

by the time you finished that, your jungle is probably full so go back and empty it

take care : the ennemy jungle might want to get his vengence

The good position for a nice gank is when the ennemy has gone more than halfway through the lane so you should nock him back towards your allies with your Devastating Charge

If you're level 6 you can also engage with your Onslaught of Shadows , you can also ult to finish the ennemy if he is getting away

now just do what you want , you can stay in the jungle to try and finish your build or you might try to teamfight to victory :D
That might not be the best way to play Hecarim , but i'm not a pro and i like playing him dis way so i hope you like it :D
Well that's all , have a nice time playing hecarim :D