Step 1: Rough Design

Start by creating a new model file in NX. (File → New: Choose Model/Modelling).
Then, make a new sketch drawn in the XZ-plane (Insert → New Sketch: choose XZ-plane with your mouse).
Draw two lines 25 mm in length, starting at the origin. The angle between the lines should be 40°. These lines will help to align the channels in later steps.
Lastly, click on “Finish Sketch” located in the bottom toolbar.

Insert a revolved part (Insert → Design Feature → Revolve).
Click on the “Sketch Selection” item in the new “Revolve” menu. A new sketch should appear. Choose the XZ-plane again.
Now sketch two circles (Insert → Curve → Circle) with origin (0,0) and diameters of 50 mm and 56 mm, respectively.
To go back to the "Revolve" menu, click on "Finish Sketch" again (the button is in the upper left corner now).

Then choose the vector to be the Z-vector (should be blue) and the point to be the point of origin.
The angle should start from 0° until an angle of 360°.
Finalize by clicking on OK.

Hide the hollow sphere by right-clicking on the “Revolve (2)” item in the part navigator (left panel). Choose “Hide” and the sphere is now hidden.
Insert an “Extrude” part (Insert → Design Feature → Extrude).
Click on “Sketch Selection” item in the “Extrude” menu. A new window (“Create Sketch”) will open. In the type section, choose "On Path".
Then choose the sketch-line at 40° drawn before. Set "Arc Length" to 0 mm and click "OK". The view will now turn.
Draw another circle with origin (0,0) and a diameter of 12 mm.
Click on “Finish Sketch” after you are done.

To create the middle channel, repeat the steps used to create the first channel.
This time, choose the guide line perpendicular to the sphere.

To make the left channel, we can just create a mirrored copy of the right channel.
Copy the geometry (Insert → Associate Copy → Instance Geometry).
Click on Select Object and then choose the cylinder at 40°.
Specify the vector to be the Z vector (vertical axis) and the point to be the point of origin.
Set the "Angle" to 180° and the "Number of Copies" to 1.
Finalize by clicking on "OK".