Yes, you need a pre-test post-test design. Assume, for example, that at the end of the experiment you find that the children in group 1 are capable of a greater delay of gratification than the children in group 2. If you only have one post-test, this would be compatible with different scenarios, but you would like to differentiate between them. For example:

Scenario 1:

Looking at cartoons might cause a decrease in delay for gratification among all children, but seeing unrealistic cartoons might cause a smaller decrease.

Scenario 2:

But it could also be the case, for example, that seeing cartoons causes an increase in delay of gratification among all children. But a particularly strong one among children who looked at unrealistic cartoons.

Without a pre-post test, you don't know what the treatments actually do.

Thanks for your response. I understand your points however I have concerns that I list below. If you can be so kind to respond me on these issues I will really appriciate it.

There are two practical problem with pretest.

1) Time. With prestest it will take Ta lot longer to conduct the study which would be exhausting for young children.

2) Especially children who can delay gratification to gain second marshmallow in pretest will develop expectancy for posttest which would cause difficulty to measure effect of cartoons.

Another problem is to determine lenght of duration that we would wait in pretest. How long we should wait until we provide second marhmallow?