An object is moving but we don't know its mass or velocity. a force of 20 newtons to the right
is exerted on the object for 20 seconds. what is the (vector) change in linear momentum for the
body as a result of this impulse?

The impulse is (force) x (time) = (20 N) x (20 sec) = 400 N-sec

When we grind through the units, we find that the [newton-second]
is exactly the same as the [kilogram-meter/sec] unit-wise, and once
we know that, it doesn't surprise us to learn that impulse is equivalent
to a change in momentum (mass x speed ... also kg-m/s).

So this impulse exerted on the moving object adds 400 kg-m/s of
linear momentum to its motion, directed to the right.  That may or
may not be the total change in its momentum during that 20-sec,
because our 20-N may not be the only force acting on it.