jmc

The multiples of 2 from 1 to 100 are $2,4,6,\dots ,100$. There are 50 such numbers.

The multiples of 3 from 1 to 100 are $3,6,9,\dots ,99$. There are 33 such numbers.

These lists count all of the multiples of 6 twice. The multiples of 6 are $6,12,\dots ,96$, and there are 16 such multiples of 6. Therefore there are $50+33-16=67$ multiples of 2 or 3 from 1 to 100.

All of the 25 multiples of 4 from 1 to 100 are on this list. Therefore there are $67-25=\boxed{42}$ numbers from 1 to 100 that are multiples of 2 or 3 but not 4.