Good afternoon, I have tried every setting on my Sony DSC-H400 to stop the flash reflecting back off the glass of my subject. I'm new at this! I have read through all my books.

I originally assumed you were referring to subjects in glass protected display cases, and that's what the second part of my answer refers to. The 1st part below refers to taking flash photos of people wearing spectacles.

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Flash photos of people wearing spectacles:

The main problem is that the spectacle mirrors and reflect the light.
If the flash is mounted on the camera and pointed at the subject then light will be reflected back into the camera.

(1) The most complete fix is to not use a flash and use other 'ambient' illumination whose reflections can be better controlled. This may not be practical.

(2) In place of a flash it may be possible to use an external light source.
Use of eg an LED lamp can help as you can adjust its position to move reflections out of the scene. If the subject is moving (eg fish) flash is often helpful.

(3) If flash & spectacles are unavoidable then something along the lines covered in my "glass case" situation may be suitable depending on circumstance.

(4) A flash based solution that works quite well but takes more work is to use an external flash triggered by your camera. An external flash can be located some distance to one side of the lens axis so that reflection return at an angle and do not enter the lens.

As your specific camera does not have an external flash connector less standard method are needed. Many flashes, including some low cost ones, can be triggered optically by the flash from another unit.

What I do on occasion is use an on / in camera flash set to manual low power, then diffuse it with paper or cloth of a formal diffuser so that the light reaching the subject directly is small. I mount an external flash either independently mounted or on a bracket that allows 100mm+ spacing away from the left side of the camera. While this results in manual flash operation it is useful enough in terms of power and off axis angle To be worthwhile.

Optically flashes will usually operate in manual mode - meaning that you must set the brigthts level manually. This is not as good as having automatic exposure adjustment but is still very useful and quite easy to get used to.

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Flash photos through glass in display cabinets etc.

My answer here and other answers to that question there MAY help depending on your situation. The answers in 1. above are generally applicable.

If you can mount the flash some distance from the camera so the camera does not 'see' the flash reflection directly it can help greatly.

Here is a summary of my above cited answer (with some additions) but do look at the original.

(1) Place the lens face close to the glass if possible - maybe one foot or less.

(2) Arrange the camera so it's axis is at a significant angle to the glass, so that reflections from the flash are reflected away from the camera and completely out of the scene. I usually photograph from the side but best angle depends on subject and circumstance and horizontally or vertically angled or in between is OK.

(3) Set camera so that the non flash illumination is low compared to the flash illumination. Probably at least F/8 and a smaller or much smaller aperture can help. (Too small (f/22?) and you start to get softening due to diffraction. How small is too small depends on the lens.

(4) Experiment.

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This photo 2000 years! - Xian

Temporary image while link self-repairs (hopefully).

was NOT taken with flash but there was a thick glass security cabinet (the display is priceless) and multiple halogen lamps from various angles making photos from any distance very poor.
I placed the lens essentially against the glass at an angle and shrouded my head and camera with a jacket so that there was no external light around the camera. I have some good "with flash" through glass examples which I will try to post a sample or two of.

If distance to glass is substantially lower than the lens focal length imperfections on or in the glass are defocused. They still degrade the image but usually only as somewhat reduced contrast if not too severe. (Needless to say I clean the glass well whenever possible.)

Angled flash works well for eg museum and similar display cases where flash is allowed. You can almost always get good photos of static subjects behind glass without using flash. Colour balance needs to be adjusted to suit. Use of an LED lamp can help as you can adjust its position to move reflections out of the scene. If the subject is moving (eg fish) flash is often helpful.

editing