Firstly, never put clean code in post, use Blockquote to do it. Secondly you can use this MySQL Library which include methods to INSERT, UPDATE or GET values from Database. To know basics you can watch this or this.
In my opinion your server.lua will look like this:
RegisterNetEvent('zombie:count')
AddEventHandler('zombie:cout', function()
MySQL.Async.execute('UPDATE YOUR_TABLE_NAME SET killedZombie = killedZombie + 1 WHERE steamhex = @steamhex',
{ ['@steamhex'] = PlayerIdentifier('steam', GetPlayerServerId(GetPlayerPed(-1))) },
function(affectedRows)
print(affectedRows)
end
)