As Cypress and others said above, those statements "mechanical and technical" mean the nuts 'n bolts of police/detective work. Mechanical is the step-by-step gumshoe type things that detectives do. Technical is the computer, forensic, scientific things that are done in cases. Both types of investigation work occur simultaneously with different people doing different specialty tasks.
That would include:
- conducting interviews
- looking for physical evidence in all known or suspected crime scene areas and then having any possible evidence analyzed by crime scene technicians or crime labs, along with getting basic DNA profiles of Kyron, TMH, KH and other family members so they have reference samples.
- forensic examination of computer hard drives, files, CD or other media for any and all computers TMH or KH had access to.
- going through any paper files, bank statements, financial records, phone records, receipts...all trying to piece together the movements of TMH and (probably) KH too and perhaps ancillary people like the landscaper.
- all the things that cops do including writing lots of reports, amassing case files for documentation, meeting with FBI, meeting with the DA, etc, etc.
It's not like CSI or the TV crime shows where things are miraculously solved in 1 hr. Most police work is nitty gritty tedious stuff.