Attacking with two weapons

I know we had a question about attacking with two weapons, so I would like to clarify the ruling:

As per the DMG pg 70

Attacks With Two Weapons:

Characters normally using a single weopon may choose to use one in each

hand (possibly discarding the option of using a shield). The second

weapon must be either a dagger or hand axe. Employment of a second

weapon is always ot o penalty. The use of a second weapon causes the

character to attack with his or her primary weapon at -2 and the secondary

weopon at -4. If the user’s dexterity is below 6, the reaction/attacking Adjustment

penalties shown in the PLAYERS HANDBOOK are added to EACH

weapon attack. If the user’s dexterity is above 15, there is a downward adjustment

in the weapon penalties as shown, although this never gives a

positive (bonus) rating to such attacks, so that at 16 dexterity the secondary/

primarypenalty is-3/-1, at 17-2/0, andat 18-l/O.

The secondary weapon does not act as a shield or parrying device in any

event.