Phrases in question are written in block letters.
1. They waited FOR US.
2. This program costs TWENTY DOLLARS.
3. We drove TO DENVER.
4. We worded the letter CAREFULLY.
5. They are behaving VERY INCONSIDERATELY.
6. This volcano might erupt ANY MINUTE.
Please explain why.
I think that you can remove adjuncts from the sentences without causing any "serious harm" but you can't remove arguments without making the sentence grammatically incorrect.
1. They waited FOR US. You can remove FOR US without any problem. Sentence "They waited" is grammatically correct. (it should be adjunct then)
2. This program costs TWENTY DOLLARS. The cost of the program HAS to be in the sentence because you can't say "This program costs." (it should be argument then)
Not very sure about others. I think 5 is argument and 6 is an adjunct
Actually you can check adjunct/argument by "do so" replacement but I can't remember it well....