Ok this is my last hope, I totally don't get this question. Suppose you have one beaker of H2O at a certain mass and temperature and another beaker of H2O at a different mass and temperature. You then pour these two beakers into one separate beaker. How do I figure out the final temperature that I end with?

You would have done MUCH MUCH MUCH better to have used numbers instead of trying to summarize in vague terms. Here is what you do. Call beaker 1 stuff 1 and beaker 2 stuff 2, then,

[mass1 x specific heat 1 x (Tfinal-T1initial)] + [mass2 x specific heat2 x (Tfinal-T2initial)] = 0
Fill in all of that "stuff" and the only unknown will be Tfinal. Solve for that.