Find the mass of O degrees Celsius ice that 10g of 100 degrees Celsius
steam will melt completely?

mass is always conserved.

you have the same mass of water as you have of steam.

You need to know the heat content of 10g of steam at 100 °, and divide
by the latent enthalpy of fusion of ice (per gram).  Have a read here
(http://www.physchem.co.za/Heat/Latent.htm) for some ideas.

The steam releases 10 g * 2260 J/g = 22600 J of latent heat when it
condenses to water at 100 C.  The water releases 10 g * 100 C * 4.186
J/gC = 4186 J of heat when it cools to 0 C.  So about 26800 J of heat
is available to melt ice.  You can melt (26800 J)/(334 J/g) = 80.2 g
of ice.