Draw the reaction mechanism for the formation of ethanol from bromoethane and water and name the mechanism.

The first step is the draw out the molecules in question to understand what is happening in the reaction. You can see that the bromine atom has been substituted for an alcohol group (OH) in the enthane molecule. Water has a lone pair of electrons on oxygen and so can act as an electron donor (nucleophile) to the carbon bonded to the bromine to help the substitution reaction along.

From this knowledge, you can use your curly arrows to draw the lone pair on Oxygen of the water to attack the carbon atom bonded to bromine. But, carbon can only have 4 bonds and so you need to break one bond. We are hoping to lose the bromine atom and so you should break the C-Br bond with a curly arrow pointing to Br. You now have a the molecule CH₃CH₂O⁺H₂. You need to take a hydrogen from the Oxygen to stop making it positive charge and so that the O only has 2 bonds. Another water molecule can act like a nucleophile and a curly arrow is drawn from the water O to one of the H's attached to the ethanol molecule. Another curly arrow is drawn to break the O-H ending the arrow at O to give it's lone pair of electrons back. You now have CH₃CH₂OH, the desired molecule. The by-products are Br^- and H₃O⁺

As to name the mechanism, you know there are nucleophiles involved and it is a substition and so the mechanism is called: nucleophilic substitution.