He called the resulting system Thought Field Therapy and began training the therapists in using an algorithms and diagnosing the underlying problems before the treatment might begin.
a)began training the therapists in using
an algorithms and diagnosing the underlying problems before the treatment might begin
(Algorithms are plural. So usage of an is wrong)b)
began to train the therapists to use algorithms and
diagnosing the underlying problems before the treatment would begin
(Portions in red should be in parallel form)c)began training the therapists in using algorithms and diagnosing underlying problems before the treatment could begin
(Correct)d)began training the therapists in how to use algorithms and diagnose underlying problems before the treatment
can begin
(Event is related to past. So usage of can is wrong)e)began training the therapists in using algorithms and diagnosing underlying problems
till the treatment should begin
(Changes the meaning of the sentence)Kudos please if you like my explanation!