Can an object of a simontaniously have an instataneous velocity of 9.8 ms in one direction and an acceleration of 9.8 ms squared in the same or opposite direction?
Simply, yes. I'm assuming we're talking hypothetically, otherwise it would be very dificult to measure.
Depending on the starting velocity and the amount of time the object has been moving, there is no reason why at some point the velocity and acceleration cannot have equal magnitudes.
An object is moving at a fixed velocity of 9.8ms. At time t, a force is applied to it to create an acceleration of 9.8m/s^2) (in any direction). Now at the instant t, before it has had a chance to change velocity, both requirements are met.
Example 2, more simply:
The velocity 9.8ms much have been given because it is approximately equal to the acceleration due to gravity near the earth. If an object is dropped near to the earth's surface, assuming no air resistance, it will start at 0ms (not moving) and accelerate at 9.8m/s^2, ie for every second it is accelerating, it will speed up by 9.8m/s. Therefore, after 1 second, it will be travelling at exactly 9.8m/s.
For going in the opposite direction, think about what happens when you throw a ball upwards, where the aceleration due to gravity is downwards.
Be careful with your units. ms usually signifies metres x seconds, whereas velocity is metres per second, or metres divided by seconds, m/s or ms^-1