This isn't as straightforward as it seems. Following the textbook rules, it should be this: My friend said she would have graduated from high school by the following June. This implies that the whole time period is now in the past, and that your friend didn't in fact graduate as expected. If you are doing a grammar exercise, the above sentence is probably what your teachers are expecting. However, in the real world, if 'next June' really is next June ( June 2017), you'd need to keep the same form to preserve the sense - 'My friend said that she'll have graduated from high school by next June.'