These are the terms used when the six internal spheres are described:
Eye-sphere, ear-sphere, nose-sphere, tongue-sphere, body-sphere.
The corresponding objects are:
Form-sphere, sound-sphere, odour-sphere, taste-sphere, tactile-sphere.
We know that "mano" is mind (in some sense) so "mind-sphere" seems correct for manayatana.
And "mind-object-sphere" seems to be the best translation of dhammayatana.
Some have translated it as "mental-phenomena."
The question is: What is a mind-object (dhamma)?
1. Is it anything that one can see in ones mind?
2. Or is it the object that the mind is attending to?
For example, any feeling which arises must be a feeling about something, any
desire is a desire for something, any clinging is a clinging to something.
That "something" is the object that the mind is attending to.
Often, we do not see this mind-object. We see an external object and a feeling
arises. We do not notice that we have created a mind-object to "stand-for" or represent the actual external object.
The mind-objects that we create represent rupa things, or arupa things.
The rupa things can be divided into five classes, eye and visible objects,
ear and sounds, and so forth. Which then leaves the arupa things for a sixth
category, mind and mental-objects.
In the formula of Dependent Origination the last eight items can be seen as
the mind and its object. Contact is the contact of the mind with the object.
Feeling, craving, clinging and so forth, are what arises in the mind due to
the object. All the objects are at the level of the item "six-spheres" either
in it or associated with it (the six external spheres).
The ability to see oneself creating these mind-objects is the ability to
see dhammas. To see these dhammas, and everything which arises from them, is
to see the teaching (dhamma).