Question

1) Charles IV est mort sans héritier.

Answer 1

1) Charles IV est mort sans héritier.
True

2) Explain the grammar in this sentence:

Je veux que mes cousins puissent voyager

Answer 2

Hi !

1- Charles IV est mort sans héritier.
TRUE

2) Explain the grammar in this sentence :
"Je veux que mes cousins puissent voyager."
"Puissent" is the subjunctive tense of the verb "pouvoir".
SUBJUNCTIVE TENSE
Usually, you must have two different persons in the main clause and the dependant clause. (otherwise you would use infinitive = je veux pouvoir voyager (I want to be able to travel))
The verbs + que + subjunctive usually express = wish, order, likes or dislikes,regrets, doubts....
Many expressions are followed by subjunctive as "il faut que", "il vaut mieux que", "afin que", "bien que", "quoique", "pourvu que", "avant que"..........

Exemples =
je regrette qu'il ne puisse venir (I regret that he cannot come)
Il faut que tu apprennes ta leçon ( you have to learn your lesson)

hope I helped a little :)