An old-fashioned English way of saying "with that" or "for this" is "therewith" or "herefore". We call this a pronominal adverb.
In Dutch, this old-fashioned form is compulsory.
This is what happens:
| preposition + dit/deze
| 
| hier+preposition
|
| preposition + dat/die
|
| daar+preposition
|
Note that this only applies to independent demonstrative pronouns. A pronoun that precedes a noun (e.g. 'this book', 'that day ) is not independent. The examples below will illustrate the idea.
Recall that we use dit and dat for het-nouns, deze and die for de-nouns (including all plural nouns).
Examples of dit and deze turning into hier
Deze (singular) -> hier
| Ik heb van deze ervaring geleerd.
| I have learned from this experience.
|
| Ik heb hiervan geleerd.
Not: Ik heb van deze geleerd.
| I have learned from this.
|
Deze (plural) -> hier
| Ze schreef over deze gebeurtenissen.
| She wrote about these events.
|
| Ze schreef hierover.
Not: Ze schreef over deze.
| She wrote about these.
|
Dit (always singular) -> hier
| Ze werden door dit nieuws verrast.
| They were surprised by this news.
|
Ze werden hierdoor verrast.
Not: Ze werden door dit verrast.
| They were surprised by this.
|
Examples of dat and die turning into daar
Die (singular) -> daar
| Hij ergerde zich aan die stank.
| He was annoyed by that smell.
|
Hij ergerde zich daaraan.
Not: Hij ergerde zich aan die.
| He was annoyed by that.
|
Die (plural) -> daar
| Ze zaten achter die gordijnen.
| They were behind those curtains.
|
Ze zaten daarachter.
Not: Ze zaten achter die.
| They were behind those.
|
Dat (always singular) -> daar
| Ze praten over dat verhaal'.
| They are talking about that story.
|
Ze praten daarover.
Not: Ze praten over dat.
| They are talking about that.
|
Questions? 
