How do you see your assistant who forgets to do some of the tasks you assign to him/her? how do you treat the situation?

Every employee is expected to fulfill their duties with responsibility.
In such a situation, i might assign the task through Outlook and follow up, based on the priority of the task.
However this is not feasible on a long run and the employee has to take up the responsibility of doing the tasks assigned to, with minor follow ups or without such spoon feeds all the time.
If the employee tends to forget continuously after enough reminders, corrections, then i would also think of assigning such tasks to a different person who is more responsible or replacing this employee with another one.

I would definitely support him as he might be over loaded, delegating tasks and distributing loads works pretty well.
Forgetting too much = overload.
i have to treat my employee fairly.

Firstly I would take the task and after finishing the task analyze the situation why he/she forgot to performing the assigned task.
Because it is their responsibility for fulfilling all the assigned duties as well..

First i will get to know why he/she didnt do the task.
I will sit with him/her and discuss about his/her task list and ask him/her why she didnt do the job.
If the reason is justified then i will understand and will ask him/her to do the job right away, but if he/she didnt do the job for such reason which is unacceptable then i will give her a verbal warning and warn the latter that such mistakes will not be tolerated in the future.

He might have some priorities apart from his work tasks.
using his weekly planner agenda is important.

I would try to find out what is the reason she forgets to do some of the assigned tasks.
Is it's a leak of professionalism from her side to fulfill her duties or there was another (plausible) reason this happened.
Some tasks can be assigned trough Outlook, with reminder but I would appreciate her to work with an agenda so she can follow-up with the assignments step by step to make sure nothing will be missed.
If forgetting becomes a constant and serious issue, and no changes after discussions, than there is a possibility that she is not the relevant person for this position, I might take into consideration the replacement.

 forget once, easy to have a corrective action but  to forget continuously would think of reassign another job to him or fire him

I think that the training and follow-up list of tasks on a daily basis and held accountable to the default will solve the problem

Having worked in Jeddah as the only person speaking English as a first language this was a common problem.
The best solution is patience and understanding and make sure that he/she repeats to you that he/she understands the tasks that he/she has been set.
I often had to use a visual tool to make myself understood.
I also found that the common use of humour also eased the situation and put him/her at ease and reduced the pressure to walk away without fully understanding the situation

when i choose assistant to me the first thing he dont forget and if he forget :) i learn him how to make notes :D on mobile and reminder

We are talking about a person, who forgets to do some of the tasks you assign to him/her.
What I understood from the question is that, this person repeatedly keeps forgetting to do his/her job.
That means he/she has already been admonished several times.
Now the question is, how long, as a manger, would you continue let the organization suffer on account of this worker? It is time when I would say, enough is enough, and either give this person a lesser important position, if available, or replace him w.i.e.