If the lawyer we hired caluculated the prision terms on my boyfriends charges and came up with a low term of 6 years and a high of 13 years, is it appropriate for the DA to offer 20 years as a deal on a plea bargain? Our lawyer has no idea where he came up with that number
There is no way to give you a meaningful answer to this question.
Maybe the lawyer you hired made a mistake in calculation. Maybe the DA is considering additional charges that could be filed, but haven't been added yet.
In cases where I believe the DA has made an unreasonable offer, I do my own investigation and research, then explain why I believe my client deserves something better.
However, in your boyfriend's case, his lawyer has all the information and is in a better position to give advice than a stranger on the Internet who knows nothing about the facts.