Cachi Adentro is a tiny village to the west of Cachi, approaching the Nevado de Cachi mountains. The tourist office claims it's 7km from the Cachi, while a signpost as you leave Cachi indicates that it's 4km. We walked there and back and estimate it at 6km. Whatever the distance may be, it makes a good day hike from Cachi.
Using the map from the tourist office it's easy to find your way. You pass through the hamlet of Fuerte Alto after about 3km along the unpaved road. The same road continues to Cachi Adentro, and the views along the way are superb - it's mostly blue, sunny skies and high mountains in the distance. You'll meet plenty of friendly, curious locals along the way too.
There are few facilities in Cachi Adentro so I would recommend you bring lunch from Cachi before you leave. Cafe Oliver on the main square in Cachi sell cheap, delicious sandwiches. Also, if it's a hot day make sure you take lots of water and sun-screen. It was close to 35 degrees on the day we did the hike and even though the return trip was only 12km we were absolutely shattered by the end, and had used up 4 litres of water. There's very little shade along the route as well so early morning or late afternoon is the best time to hike in summer.