Nested Crossjoin Quadrupled my Data

There is nothing wrong with nested CROSS JOINs and they will work as intended.

I do recommend a slightly different technique for debugging.  

I haven't changed any of your code, just broken out the tables so it's easier to see what is going on.

The final RETURN statement can be updated to be RETURN T1  or RETURN T2 etc so you can see how the data looks as you walk through the debugging.

So try this

Get Total Hours = 

Var T1 = FILTER(
				CROSSJOIN(table_a,table_b),
				table_a[employee_id] = table_b[employee_id] &&
				table_a[start_date] >= table_b[date_effective_start] &&
				table_a[start_date] <= table_b[date_effective_end] &&
				table_a[start_date] >= table_b[date_production]
					)
				)

Var T2 = 	FILTER(
		CROSSJOIN(table_c,T1
			,
		table_a[str_buid_state_code] = table_c[str_buid_state_code] && 
		table_a[start_date] >= table_c[date_effective_start] && 
		table_a[start_date] <= table_c[date_effective_end]
              )

Var T3 = 
SELECTCOLUMNS(T2
,
	"Field Name 1", table_a[start_date],
	"Field Name 2", table_a[employee_id],
	"Field Name 3", table_b[supvsr_id],
	"Field Name 4", table_c[sys_description],
	"Field Name 5", table_a[duration], //this value Quadrupled
	"Field Name 6", table_c[flag_a],
	"Field Name 7", table_b[id_dept],
	"Field Name 8", table_b[id_role],
	"Field Name 1", table_b[flag_active_employee]
			)


Return T3

But I would probably create a SUMARIZE table of T2 which removes the duplicating durations.