durchgehend
continuous
In terms of time, without interruption; uninterrupted.
Die Rezeption des Hotels ist durchgehend besetzt.
The hotel reception is staffed continuously.

continuous / throughout
Loading your saved state.
continuous
In terms of time, without interruption; uninterrupted.
Die Rezeption des Hotels ist durchgehend besetzt.
The hotel reception is staffed continuously.

The word is made up of 'durch' (through) and 'gehend' (present participle of 'gehen' (to go)). The literal meaning 'going through' helps you understand the core idea of uninterrupted continuation in time or space.
Eine durchgehende rote Linie markiert den Radweg.
A continuous red line marks the bike path.
'Durchgehend' (continuous/throughout) can stand as an adjective before a noun or as an adverb describing a verb or a whole sentence. As an adverb, it often stands after the verb or at the beginning of the sentence for emphasis.
Wir haben eine durchgehende Arbeitszeit von 9 bis 17 Uhr.
We have continuous working hours from 9 a.m. to 5 p.m.
In its time-related meaning, 'durchgehend' (continuous/continuously) is often combined with services or states. Typical phrases are 'durchgehend geöffnet' (open continuously), 'durchgehend besetzt' (staffed continuously), or 'durchgehend erreichbar' (available continuously).
Unser Kundenservice ist telefonisch durchgehend erreichbar.
Our customer service is continuously reachable by phone.
In its spatial meaning, 'durchgehend' (direct/continuous) often describes transport connections. Common combinations are 'durchgehender Zug' (direct train), 'durchgehende Flugverbindung' (direct flight connection), or 'durchgehende Straße' (continuous road).
Gibt es einen durchgehenden Flug nach Lissabon oder muss ich umsteigen?
Is there a direct flight to Lisbon, or do I have to change planes?
In the meaning 'ausnahmslos' (without exception), 'durchgehend' (consistently) is used as an adverb to describe a general tendency. It then often modifies an adjective or describes the quality of an action.
Die Schüler haben in der Prüfung durchgehend gute Ergebnisse erzielt.
The students achieved consistently good results in the exam.
direct
'direkt' and 'durchgehend' can both have to do with routes or time. 'direkt' emphasizes that there is no detour or waiting time. So you reach something by the shortest route or immediately. 'durchgehend' emphasizes that something is not interrupted, for example opening hours or a connection without changing trains. Learners may confuse the words because both can sometimes seem to mean 'without interruption or change'. A practical tip: 'direkt' is about the fastest or immediate route, while 'durchgehend' is about a line or period of time without a break.

Die Apotheke ist am Samstag durchgehend bis 18 Uhr geöffnet.
The pharmacy is open continuously until 6 p.m. on Saturday.
Vom Bahnhof fährt ein direkter Bus zum Krankenhaus.
There is a direct bus from the train station to the hospital.