public ArrayList<Section> parse(JSONObject jsonObject)  {
        Log.d("myLogs", "start parse");

        ArrayList<Section> list = new ArrayList<Section>();
        Location startGeo;
        Location endGeo;
        JSONArray results = jsonObject.optJSONArray("routes");
        JSONObject route = results.optJSONObject(0);
        Log.d("myLogs","1");
        JSONArray legs = route.optJSONArray("legs");              //<---ОШИБКА!
        Log.d("myLogs","2");
        JSONObject leg = legs.optJSONObject(0);
        Log.d("myLogs","3");
        JSONArray steps = leg.optJSONArray("steps");
        Log.d("myLogs","4");

        for (int i=0; i < steps.length(); ++i) {
            JSONObject step = steps.optJSONObject(i);
            JSONObject startP = step.optJSONObject("start_location");
            JSONObject endP = step.optJSONObject("end_location");
            JSONObject polyline = step.optJSONObject("polyline");
            String encodedPoints = polyline.optString("points");

            startGeo = new Location("");
            endGeo = new Location("");

            startGeo.setLatitude(startP.optDouble("lat"));
            startGeo.setLongitude(startP.optDouble("lng"));
            endGeo.setLatitude(endP.optDouble("lat"));
            endGeo.setLongitude(endP.optDouble("lng"));

            list.add(new Section(startGeo.getLatitude(), startGeo.getLongitude(), endGeo.getLatitude(), endGeo.getLongitude() , encodedPoints));
        }

        Log.d("myLogs", "end parse");
        return list;
    }

JSONObject route = results.optJSONObject(0);

public class Section {
    private Double startLatitude;
    private Double startLongitude;
    private Double endLatitude;
    private Double endLongitude;
    private String encodedPoints;

    public Section (Double dLatitude, Double dlongitude, Double eLatitude, Double elongitude, String sencodedPoints){
        this.startLatitude=dLatitude;
        this.startLongitude=dlongitude;
        this.endLatitude=eLatitude;
        this.endLongitude=elongitude;
        this.encodedPoints=sencodedPoints;
    }

}

<?xml version="1.0" encoding="utf-8"?>

<FrameLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:id="@+id/mainlayout"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent">

    <fragment xmlns:android="http://schemas.android.com/apk/res/android"
        xmlns:tools="http://schemas.android.com/tools" android:layout_width="match_parent"
        android:layout_height="match_parent" android:id="@+id/map" tools:context=".MapsActivity"
        android:name="com.google.android.gms.maps.SupportMapFragment" />

    <Button
        android:id="@+id/test"
        android:text="Построить"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_gravity="bottom|right"
        android:clickable="true"
        android:onClick="OnClickTest" />
</FrameLayout>

    <fragment xmlns:android="http://schemas.android.com/apk/res/android"
        xmlns:tools="http://schemas.android.com/tools" android:layout_width="match_parent"
        android:layout_height="match_parent" android:id="@+id/map" tools:context=".MapsActivity"
        android:name="com.google.android.gms.maps.SupportMapFragment" />