Here is an updated version in which I've clarified the Bahubbiihi section:
It can sometimes be difficult to know which type of compound we are
dealing with. Here is an algorithm that can help you to figure out the
compound type. When you think that you have found the correct compound,
consult the above compound guide to double check:
*1.* If the compound is composed only of numbers as members and the
first number is larger than the second then it is a dvanda; if the
second number is larger then it is a digu.
*2.* If the compound starts with a number and is followed by a
non-numeral, there are two possibilities. If the two members would be in
the same case if they were to be separated, then the compound is a digu;
if the two members would be in different cases, then it is a tappurisa.
*3.* If the compound starts with an indeclinable that qualifies a
following noun in the compound, and the whole compound is acting as an
adverb, the compound is an avyayiibhaava.
*4.* For all other compounds, try to determine the case of the last
member as well as what the case of the first member would have been, had
it not been compounded with the last.
· If the cases would certainly differ, see 5 below
· If the cases would certainly be the same, see 6 below
· If it is impossible to tell for sure, see 7 below
*5. * If the cases certainly differ, then it is a tappurisa compound.
*6.* If the cases would certainly be the same, then it is a
kammadhaaraya or a dvanda. A dvanda will have two or more words that
don’t qualify each other but are simply being added together as with the
word “and” between them. In a kammadhaaraya, however, the first member
of the compound will help to qualify the final member.
*7. *If it is impossible to tell the cases of the parts of the compound,
then it may be a tappurisa or kammadhaaraya compound and context and
doctrinal familiarity should be your guide to figuring out the solution.
Not all compounds are easily analyzed.
*8.* If you have a compound that fits the “type” of one of the above
compounds but the last member is a noun, or is used as a noun, but yet
this last member is agreeing (case, gender, number) with an external
noun as would an adjective, regardless of its normal gender, etc., then
you are dealing with a Bahubbiihi compound. Such a compound will have an
extocentric focus and be "possessed" by an external noun rather than
having a relationship to it via simple apposition.
Please see the above sections on compounds for more thorough information.