Proportion expected to breed true?

Why don't you make a Punnett square to find out? true breeds should have genotype RRGG (we don't care about the height).

Since we don't care about the height, we don't need to involve it at our Punnet square:

As you said, the crossing is RrGg x RrGg (we don't need the Tt)
So, the possible gametes are RG Rg rG rg (for both parents)
So, the Punnett should be:

           RG         Rg           rG          rg

RG    RRGG    RRGg      RrGG     RrGg
Rg     RRGg     RRgg      RrGg      Rrgg
rG      RrGG     RrGg       rrGG      rrGg
rg      RrGg       Rrgg       rrGg       rrgg


As you see, only 1/16 plants produce round green seeds AND are breed true.
However, the exercise asks something else:
We need to find all the plants that produce green and round seeds (true breeds or not): they are:

           RG         Rg           rG          rg

RG    RRGG    RRGg      RrGG     RrGg
Rg     RRGg     RRgg      RrGg      Rrgg
rG      RrGG     RrGg       rrGG      rrGg
rg      RrGg       Rrgg       rrGg       rrgg

They are 9. Out of them, only one breeds true.
So, the answer is: 1/9 plants with round and green seeds are expected to breed true.

1/9 isn't the answer, unfortunately...

Whops, wait a second, the G allele is the dominant for the color yellow? Who named it as G ?... Anyways...
Let's do this again:

           RG         Rg           rG          rg

RG    RRGG    RRGg      RrGG     RrGg
Rg     RRGg     RRgg      RrGg      Rrgg
rG      RrGG     RrGg       rrGG      rrGg
rg      RrGg       Rrgg       rrGg       rrgg

Firstly, we count the plants with round GREEN seeds. That is, plants with genotypes RRgg or Rrgg:

           RG         Rg           rG          rg

RG    RRGG    RRGg      RrGG     RrGg
Rg     RRGg    RRgg      RrGg      Rrgg
rG      RrGG     RrGg       rrGG      rrGg
rg      RrGg      Rrgg       rrGg       rrgg

They are 3. Out of them, only one is breeding true: The RRgg. So, the answer is 1/3.

Well, I was wrong but you shouldn't just copy paste the answer without understanding how it is done. You should've been able to find the mistake on your own.

That's correct, thank you! I'd been struggling with that problem for so long that I think I forgot how to look at it, but your description was very helpful. Thanks again.