Line segment AM is congruent to line segment MB, but M is not the midpoint of line segment AB. How would this be drawn?

Two line segments are congruent if they have the same length. They
need not form any particular angle or be perpendicular or parallel. Instead of directly
saying that two line segments have the same length, the term congruent is used in
geometry when defining two line segments that have the same
length.

Here, line segment AM is congruent to line segment MB. AB is
the line segment that you want to draw but it is given that M is not the mid point of
AB; this means that M does not lie on AB as it would then be the mid point of
AB.

From the information provided it is not possible for you to draw a
unique line AB. There can be an infinite number of ways in which AB can be
drawn.