How to analyze this opamp circuit?
Premises about the op. amp.:

zero input current
infinite gain (V+ = V-)
zero output resistance
no input/output voltage restrictions

First part is a simple voltage divider:

$$V_+ = V_{in}\frac{R}{3R} = \frac{V_{in}}{3}$$
The other is a also a voltage divider with equal resistors:

$$ V_- = \frac{V_{out}}{2}$$
Since V+ = V-:
$$ V_{out} = \frac{2 V_{in}}{3} $$