This is the original text:
Die USA und China stehen am Anfang einer gefährlichen Konfrontation. Ihre wirtschaftlichen, militärischen und politischen Interessen sind in dieser Weltordnung nicht mehr vereinbar.
Peking und Washington müssen mit dem Aufbau einer neuen beginnen.
And here is the translation:
The US and China are at the beginning of a dangerous confrontation. Their economic, military and political interests are no longer compatible in this world order.
Beijing and Washington must start building a new one.
The parts of speech in the last sentence are:
- Peking und Washington → Beijing and Washington
- müssen → must
- mit dem Aufbau → building (literal: "with the building of")
- einer neuen → a new one
- beginnen → start
But German word order is different from English word order. German word order gives much more freedom to many parts of speech than English word order, but the rules for the positions of the verbs are very restrictive.
The verb of a German sentence often consists of more than one word. This is equal to English. In both languages you can add auxiliary verbs or also modal verbs to full verbs, and this also is the case in your example:
- full verb
beginnen = start
- modal verb
müssen = must
Only in German you also can have separable verbs. A separable verb is a word, that can be split into two parts in necessary. An example of a separable verb is vorbereiten (to prepare).
Here are some rules for positioning of German verbs in German statements (there are different rules for questions and commands):
- Exactly one word of the verb must be inflected, this means it must match with the subject in these categories:
- number (singular or plural)
- person (first, second or third person)
- The same word must be inflected to represent the grammatical tense of the sentence (present tense, future tense, ...)
- The same word must be the second part of speech within a sentence.
- If the verb consists of only one word, and if it is non-separable, than everything is clear now: You have just one word. It must be inflected and it must be the 2nd part of speech. But if you have an auxiliary or a modal verb together with a full verb, or if your word is a separable verb, then you need these additional rules:
- If there is an auxiliary or a modal verb, then the rules #1 to #3 apply to it. If the full verb is separable, then it must not be separated (so you have to use it in its one-word form in this case). See rule #7 for the full verb.
- If there is no auxiliary verb and no modal verb, and if the full verb is separable, then you have to split this verb into its two part. The main part (i.e. not the prefix) is the word that must obey the rules #1 to #3. The prefix must be handled according to rule #7.
- If you had to apply rule #5 or #6, then there is something left. This is either a full verb (if you had to apply rule #5) or the prefix of a separable verb (if you had to apply rule #6). In both cases this word must stand at the very end of the sentence. This part will not be inflected, i.e. if it is a full verb, it has to stand there in its infinitive form. (It's impossible to inflect the prefix anyway.)
In your example you had a modal verb (müssen) together with a non-separable full verb (beginnen). This means: The part, that must stand on position 2 and that must be inflected is müssen.
The plural present tense form of müssen in the 3rd person is: müssen
Because we had a modal verb, we did apply rule #5, and so the full verb (no matter if separable or not) must stand at the very end in its infinite (i.e. non-inflected) form, and so we get:
Peking und Washington müssen mit dem Aufbau einer neuen beginnen.
An example with a separable verb:
Markus prepares his car for the expedition through the dessert, which he has announced on his YouTube-Channel.
This is a separable verb. The separable prefix is vor and the main part is bereiten.
Here we have no auxiliary verb and no modal verb, but the full verb is separable, so we need to apply rule #6 and we get:
Markus bereitet sein Auto für die Expedition durch die Wüste, die er auf seinem YouTube-Kanal angekündigt hat, vor.
If you add a modal verb, you get:
Markus wants to prepare his car for the expedition through the dessert, which he has announced on his YouTube-Channel.
Markus will sein Auto für die Expedition durch die Wüste, die er auf seinem YouTube-Kanal angekündigt hat, vorbereiten.
If you shift the sentence into another grammatical tense, you also have to add an auxiliary verb:
Markus did want to prepare his car for the expedition through the dessert, which he has announced on his YouTube-Channel.
Markus hat sein Auto für die Expedition durch die Wüste, die er auf seinem YouTube-Kanal angekündigt hat, vorbereiten wollen.
So, if you have both, an auxiliary verb plus a modal verb, then it is the auxiliary verb that must obey rules #1 to #3, and at the end of the sentence you have the full verb followed by the modal verb.