(2√8)*(-3√8)
= (2*(-3))*(√8)*(√8)
= -6*8
= -48
The product is the product of all the factors. The properties of multiplication let you put these in any convenient order. The product will be negative if there are an odd number of minus signs (as here).
A square root times itself is equal to what's under the radical. (That's the definition of a square root.)