The 78 kg astronaut floating in space throws a 4.3 kg rock with a velocity of 3.7 m/sec. As there is no air in space, the conditions are ideal for the law of conservation of momentum to hold.

The mass of the rock is 4.3 kg and it is thrown at 3.7 m/s. The momentum of the rock is m*v = 4.3*3.7 = 15.91 kg*m/s

Initially the momentum of the astronaut and the rock were 0. To maintain the sum as 0, the momentum of the astronaut should be -15.91 kg*m/s

As the mass of the astronaut is 78 kg, the velocity of the astronaut is 15.91/78 = -0.2039 m/s. The negative sign shows that the astronaut moves in a direction opposite to the direction of the stone.