I'm thinking that the maximum without quality loss should be 12x8, but not sure.
It all depends on your definition of "without quality loss".
There are several factors that could define that 'quality' beyond ambiguity.
I'll focus (pun intended) on resolution, because that is an important (although not the only) factor in human vision. Also, I'll assume the original file (3456x2340 pixels) to be optimal, i.e. perfectly (capture) sharpened.
At a normal viewing distance (25-30cm or 10-12in) under average illumination viewing conditions, human visual acuity is limited to approx. 5-8 linepairs/mm (it varies between individuals, some do even better). Those 5-7 lp/mm translate to 254-356 lines or pixels per inch.
We could therefore use 300 ppi as our goal for output, although higher numbers do translate into slightly better output quality on inkjet printers (I'll leave that for another discussion). As it happens, there are many output modalities that 'happen' to have similar native resolutions. For example, Fuji Frontiers use 300 dpi, Lambda Epsilons use 254 dpi, some others use 400 dpi, etc.
Taking 300 ppi as our benchmark, that would lead to an un-interpolated output size of your image file of 3456/300=11.52" by 2340/300=7.8" (or roughly A4 sized paper). Anything larger will gradually lose sharpness in proportion with increasing size.
Finally, when the output is viewed from a larger distance, the apparent resolution increases because the angular resolution of the eye remains constant. IAW, you can get away with some larger output if it is viewed from a larger distance.
Now, this may lead to the need for interpolation of the original file size to something larger, to accommodate the baseline 300 ppi criterion for the output modality of choice. The interpolation will not improve actual resolution, but it can help to avoid the creation of ugly artifacts that are dead giveaways of lacking resolution. It can also mimic resolution by keeping edges smooth and of high contrast, which will trick human vision into thinking it is sharper than it actually is. That's when final output sharpening is useful to mask the shortcomings and create a better looking result.
Some software applications will produce better upsampled images than others. Because your 18x12 inch requirement isn't that drastically different from the 'optimal' 12x8in, it's 50% larger, you may be able to do a convincing job in Photoshop with a Bicubic smoother resampling.
However, depending on your printer, you probably will get a better result from a relatively affordable program like
Qimage because it exploits the native printer resolution and it uses better interpolation algorithms, and it sharpens to compensate for the amount of interpolation automatically. Especially if you print a lot and/or want the best quality output, Qimage is very much recommended.
Bart
