Explain how to find 14 time 19 by breaking apart the factors into tens and ones and finding the sum of the four partial product?

You could break 14 and 19 into (10 + 4), and (10 + 9). In order to find the answer this way, you would have to multiply both of the first two numbers by the other two. So you would have 10(10+9) and 4(10+9); this gives you (100+90) + (40+36), which if add together gives you 266, the answer to the problem!
You could also say 10*10+4*10+10*9+4*9, which still gives you 266. 
Hope this helps!