Problem #1
Your logic is wrong. There aren't any numbers that would be "0>=number>=10" i.e. less or equal to 0 but at the same time greater or equal to 10. The correct logic would be to look for a number that is at least 0 but not larger than 10 (0 <= number <= 10).
The same apply for the rest of the checks.
Problem #2
In many programming languages you cannot exactly use the same expressions as you'd use in mathematics. To tell the C compiler you want to check if a number is at least 0 and is no more than 10 then you have to describe this with two conditions combined together with an and (&&) operator:
0 <= number && number <= 10
Correct Code
#include <iostream>
using namespace std;
main()
{
int number;
cout << "Please enter the number between 0 to 30: ";
cin >> number;
if (0 <= number && number <= 10)
{
cout << "Blue";
}
else if (11 <= number && number <= 20)
{
cout << "Red";
}
else if (21 <= number && number <=30)
{
cout << "Green";
}
else
{
cout << "It is not a correct colour option.";
}
}