Answer
The statement is false.
One way to make it true is to replace the word
"four"
with
"at most two"
Work Step by Step
A line and circle can have
- no intersections
- one intersection (the line is a tangent line to the circle)
or
- two intersections (the line is a secant of the circe).
In no way can there be 4 (real) intersections.
So the statement is false.
One way to make it true is to replace the word
"four"
with
"at most two"
so it reads
"... circle and and a line can have at most two real ordered-pair solutions.'