Write an expression with the five terms containing the coefficients 12 15 18 and 21

Let the variable used in the expression be "x".

Since the desired expression should contain 5 terms, therefore the powers of "x" will be as follows:
x^0 , x^1 , x^2, x^3 and x^4 where x^0 = 1 and x^1 = x

Now we are given only 4 coefficients to use, so we will have to assume a fifth assume.
Assume the fifth coefficient to be 7

It is a convention to write the powers in an expression in descending order, so the expression will be as follows (without coefficients):
x^4 + x^3 + x^2 + x + constant

Now add the coefficients in any desired order since there are no conditions, the final expression can be written as follows:
12 x^4 +15 x^3 +18 x^2 + 21 x + 7