Most likely, your issue seems to be with unsupported Android SDK version as per Ti SDK you are using.
So before doing anything, try to grab what this page says to know all about software compatibilities: Titanium Comptability Matrix
It says that minimum Android version as of latest Ti SDK 6.x.x is API 16.
Now, follow these steps carefully to get a fresh start on your system.
- First of all, download Android latest SDK from here: Android SDK
- Unzip it & put it in at some simple path like in /Users/username/android-sdk
- Download Appcelerator Studio (AS) & install it. It will download all pre-requisites like Java, Python
- Open Appcelerator Studio & go to Preferences->Studio->Platforms->Android. Select the path of android sdk you unzipped in step 2.
After all these steps, you can open Android SDK Manager (see screenshot where it is) & install necessary SDK, Tools, etc.

Note: I do not suggest to download SDKs via AS as I have faced path issues in beginning.
Even if these steps do not help you, then provide us the log output after running this command on terminal: appc info
If terminal says this command is not found, then you need to go through the AS installation properly.