$(3)_4+(2)_4 =(5)_{10} =(11)_4$, that will give one carry.
Now, carry, $(1)_4+(2)_4+(1)_4=(4)_{10}=(10)_4$
So, on adding we get, $(2.3)_4+(1.2)_4=(10.1)_4 $
$(10.1)_4 \times (10)_4=(101)_4$
Or, Another way is to convert them in decimal, then after doing all calculation, convert back to desired base.
Note: In base $4$, we can only {$0,1,2,3$}, in any calculation(adding or multiplication) if get $4$ or above. It need to convert back into base $4$