Null pointer exception, "Attempt to read from field on a null object reference"

A null reference is just that null. In your code it is tasks[i].name where you try to call name on tasks[i] so tasks[i] is null.

There is one scenario I can think of, where your code would definitely throw a NullPointerException. So, I will assume your tasks array can look looks like this:

tasks = [task0, null, task2, task3, null, task5]

Then full_tasks will have a size of 4 but

for (int i=0; i <= full_tasks.length - 1; i++) {
        full_tasks[i] = new Assignment(tasks[i].name, tasks[i].days_due, tasks[i].time);
}

will throw a NPE as soon as i == 1 because tasks[1] is null.

So, if you want to fill full_tasks with only non-null tasks make sure you got the right indexes of tasks.