If cells of a multicellular organism have the same genes, how can there be many different cell types in a body?

Because of cell differentiation

Explanation:

Multicellular organisms are organisms that have many cells in their body system, unlike unicellular organisms that have just one. However, these many cells contained in a multicellular organism are of different types performing different functions.

Although they all have the same set of genes encoding the same proteins in them, they are able to become different and perform different functions via a process called CELL DIFFERENTIATION. Cell differentiation is the process whereby cells of a living organism becomes specific in their functions as they divide. This is a result of the REGULATED EXPRESSION OF GENES. The genes in each cell are not expressed at the same time, hence, they have different functions.