First off, you don't include anything!

Secondly, try the exit() function to exit within your if statement (if the number is outside of the bounds)
NOTE: This method uses the exit() function, which (I believe) is often found in <cstdlib>
but my compiler (MinGW) doesn't require it. It's best to include the libraries as good practice though.
cpp
#include <iostream>
#include <cstdlib> // for the exit() function
using namespace std;
int main () {
int x;
cout << "Enter any integer: \n";
cin >> x;
if (x < 1 || x > 32767) {
cout << "Number is outside the acceptable range of values.\n\n";
exit(EXIT_FAILURE);
}
if(x % 2 == 0)
cout << "The number is even.\n\n";
else
cout << "The number is odd.\n\n";
cin.get(); // you wasn't pausing! how is the user supposed to read before exiting?!
return EXIT_SUCCESS;
}
Hope this helps
EDIT:Alternatively, you could simply use if/else if/else structure, like so:
cpp
#include <iostream>
using namespace std;
int main () {
int x;
cout << "Enter any integer: \n";
cin >> x;
if (x < 1 || x > 32767)
cout << "Number is outside the acceptable range of values.\n\n";
else if(x % 2 == 0)
cout << "The number is even.\n\n";
else
cout << "The number is odd.\n\n";
cin.get(); // you wasn't pausing! how is the user supposed to read before exiting?!
return EXIT_SUCCESS;
}
I think that's what your instructor is looking for, but exit() might make you look like you read into it a bit