Answer: Designing a system is a process of creating components, elements, etc for a known desired outcome or specification.
Any system can be defined as below,

When desired output and available input resources are already known then a system is created in such a way that desired output can be achieved.

In the process of system design,
Both desired output, as well as available inputs, are known and a system is designed that meets the requirements.
On the other hand,
When a system is analyzed the inputs are known, the system is already in place, and output is predicted.
We will study the example of a used engine below, Let's first understand what analysis means.
Suppose I have found a used engine in a working condition and I do not know its specifications and I do not know what brand it is. I want to find out how it performs. So, I test this engine in a lab.
Suppose I have a total of 10 liters of fuel with me. But, I can only fill one liter of fuel in the engine tank at a time. So, I decide to do 10 different experiments. Each time, I put one liter of fuel in the engine and I check how much time the engine would run at a specific speed. I repeat this experiment 10 times for 10 different speeds. I plot a graph of different speeds vs engine running times. When I want to know the engine running time at an intermediate speed I can easily predict from the above data. This is nothing but an analysis of the system.
Now let's understand what designing a system means.
Suppose, I don't have an engine in the first place. I only know that I have only one liter of fuel. I also know that the engine must run at some specific speed and for the exact given amount of time. Now I design an engine (system) to meet the above specifications. This is nothing but a system design approach.