I've read that the Kelvin temperature for my screens should be around 6000K but I only have RGB values for adjusting the colors. Does anyone know what would be the best R, G, B values that match 6000K? Or a better solution to manually adjusting the two monitors I have to resemble each other for color?
Well, if there was a magic RGB setting working for all monitors in the world, there would be no need for calibration anymore, now, would there?
In order to bring your display to a given temperature, you would usually use a calibration tool like the ColorHug, Spyder, or Colormunki, for example. Those will be able to measure the light emitted by your monitor, and help you adjust the RGB settings of your monitor to get to the right temperature.
For example, dispCalGUI, in their wizard, have a step where you place the calibration device on the screen, showing a white patch, and sliders on the side to show the measured RGB levels and the white point, prompting you to adjust the RGB values of your monitor until the sliders all go to their marks.
Kelvin temperature for my screens should be around 6000K
That is uncommon, as it does not match any of the standards: photography is 5500K, DTP is 5000K, sRGB is 6500K.
RGB values for adjusting the colors
I guess you are referring to the RGB intensity control on the monitor. Due to different filters in different panels and different backlights it is impossible to say what is the right combination of RGB intensities (gains) for a particular colour temperature. Worse, different settings for those gains may result in the same colour temperature but different brightness and/or tint. The only way to know is to measure.
Measuring the colour temperature of a display, you may have a limited success using a digital camera in raw mode and shooting a screen filled with grey (something like 118/118/118 is sRGB in, say, Adobe Photoshop), shutter speed set to 1/15 or slower to avoid any flicker, aperture set so that the shots are exposed to the right, clean screen, and hood very close to the screen to avoid any reflections (fully de-focused lens is what works here). Adobe Camera Raw or some other converter will tell you the approximate colour temperature when you set white balance from the centre of the frame (it is better to have tint indication within the ±3 range). With some luck, the error may be smaller than 10%. Using a colormeter or a spectrophotometer the way matt.nguyen suggested above (or something similar, depending on the software) yields much more accurate results, with the error of 3% or less.
However colour temperature alone does not fully characterize the neutrality - one needs to take the tint (magenta-green) axis into account too. One of the easiest and most perceptually accurate ways to measure both is to use a colormeter such as those made by Sekonic or Minolta.
With any of the methods above and a bit of patience you can achieve a good match between 2 monitors, much closer than it is possible with eye-balling.
On a more general note:
If your workflow is not colour-managed, the best bet is 6500K, and the monitor set to sRGB if possible.
If it is colour-managed, you can try the "canned" monitor profile or setting your monitor to some pre-determined profile if the monitor allows it (the colour temperature in this case is also to be set to 6500K for sRGB and Adobe RGB for pre-determined profiles; or to the "default" for the canned profile; or to whatever the pre-determined profile recommendations suggest); and setting the same profile as system monitor profile.
However, unless you are working with a high-end monitor where the presets are really good and accurate, the better approach is to get a decent colormeter or spectrophotometer. Choosing such a device, in my experience it is better to be conservative. Any device that is less than 2 years on the market may bring unpleasant surprises.
If your monitor is not one of those wide gamut X-Rite DTP-94 second-hand is an excellent choice, it is very stable and may need just some cleaning and nothing else.
For wide gamut monitors X-Rite i1Display Pro is a very good choice.
Ethan Hansen has a very useful page on the comparison of monitor calibration hardware: http://www.drycreekphoto.com/Learn/Calibration/MonitorCalibrationHardware.html
I vouch for his plug for basICColor Display software, too.
During the process of calibration and profiling a decent software allows either to pre-set and calibrate colour temperature first, or to profile for "monitor native" colour temperature and gamma. I mostly opt for the latter; it is not uncommon to try different modes here and to select the one that looks best.