大きい and 多い: size or quantity
Distinguish 大きい for the size or scale of something from 多い for a large number, amount, or frequency. Do not translate every use of English big or large with the same Japanese adjective.
大きい: large in size or scale
大きい describes the size of an object and can also describe the scale of a sound, change, or influence. 庭に大きい木が一本あります。 refers to the size of one tree, while 大きい声で話してください。 refers to the volume of a voice.
It does not by itself say that several objects exist. 大きい箱が三つあります。 means that there are three large boxes; 大きい modifies the size of each box.
多い: many or much
多い evaluates a count or amount as large. この公園は朝に散歩する人が多いです。 and 今年は雨の日が多いです。 refer to the number of people and the frequency of rainy days.
Japanese commonly uses a predicate such as 人が多い to describe quantity. Nouns are modified in expressions such as 人の多い町 or 多くの人. Do not treat 多い人 as a universally valid direct translation of many people.
When size and quantity appear together
この店には大きいかばんが多いです。 says that this shop has many large bags. 大きい evaluates the size of each bag, while 多い evaluates how many such bags there are, so both adjectives can appear in one sentence.
売り上げが大きい views sales as large in scale, while 注文が多い focuses on a large number of orders. With abstract nouns, both scale and count may be possible; identify what is actually being measured.
Quick check: In この公園は朝に散歩する人が多いです, does 多い describe the walkers’ body size or their number?
Show the answer and why
It describes the number of people. Describing one person's body as large would require a separate context with a form such as 人が大きい.