Step 1: Recall the simple colour rule for litmus.
Red litmus paper only changes colour when it meets a basic substance, it stays red in both acids and neutral liquids.
Step 2: Test each test tube against this rule.
Distilled water is neutral, so it will not touch the colour of red litmus at all. The acidic solution is, by definition, not basic, so it also leaves red litmus unchanged.
Step 3: Consider the basic solution.
A basic solution carries an excess of hydroxide ions, and these are exactly what red litmus paper responds to by switching colour to blue.
Step 4: Pick the correct test tube.
Only the test tube holding the basic solution will turn red litmus paper blue. \[ \boxed{\text{Base}} \]