My girlfriend was a refused a visa to visit me in the UK. What now?

We can take things from the top...

i could not appeal or get administration review

No, there is no path for appeal in visitor applications. Administrative review is a process reserved for applicants in the tiered system, so it's irrelevant anyway. But there's clearly an ownership issue and they have picked up on it (it happens a lot), more about that later.

12 months before we can apply again???

This is not correct. A person can apply again as soon as they get their passport back from the VFS, even the same day. There is no required interval between successive applications and you can find an existing answer here: How soon can I re-apply for a UK visa after getting a refusal?

how do i get the embassy to accept what i wrote to be true?

They have not challenged your credibility. The ECO explains that she's OK on your side of things. The age difference is also OK. But again the ownership issue arises...

i have no intentions of my partner overstaying

This unveils a problem. You do not own the applicant or the application, it's not your application, it's hers. You are a sponsor and your role is strictly limited to establishing your own credibility and providing the sponsor support documents. You did that in a way that they are satisfied with, and to attempt going beyond the role of sponsor raises alarm bells for a decision-maker. Let's introduce two points that causes romantically motivated applications to fail...

1. A sponsor's responsibility is to demonstrate the capacity to maintain and accommodate the application. Nothing else. Your 'intentions' are irrelevant and attempting to assert them indicates that you do not understand what your role is and by extension that you do not understand the rules. This is a fair assumption on their part because if your friend decided to go underground and disappeared inside the UK there is nothing you could do to prevent it.

2. Even worse, you cannot attest to the applicant's intentions. The applicant is a different person and while you may be certain of her intentions, decision-makers do not accept that sort of thing. The ECO reminded your gf...

   "...the onus is on you, the applicant, to demonstrate...

The ECO went on to explain that she is basically OK with your gf's 'spravka' (that's a very good thing) but it did not apparently jive with the other stuff your gf submitted (that's a bad thing). It's likely your gf has never applied before and did not know what was expected of her.

Finally, the ECO went on to explain that the pattern of your gifts (in the form of bank transfers) suggested that your relationship was something like a kept woman who received maintenance payments from abroad. Your gf should have declared this as additional income. Paradoxically, doing that would have helped the application. Again, this type of mistake happens a lot with romantically motivated visa applications.

So the ECO concluded that your gf was not a genuine applicant or did not understand what she was doing and the risk of her going underground was unacceptably high. V 4.2 (a) & (c).

She's probably devastated and you are probably angry, scouring the net for forum advice. They don't like having upset sponsors, it's not good for their image, but the application left them no choice apparently. This is a fairly 'vanilla' type of refusal and you can engage a regulated adviser to manage her next application. I am guessing this would cost about GBP 400 - 550 (but that's strictly a guess). You can print out this question/answer along with the refusal notice and email it to an adviser and get a better estimate. A full-on solicitor can be used if you want, but isn't usually needed in these types of 'vanilla' cases; adviser versus solicitor is a matter of personal choice really.