Your interpretation of the model’s coefficients is not completely accurate. Let me first summarize the terms of the model.
Categorial variables (factors): $race$, $sex$, and $educa$
The factor race has four levels: $race = \{white, black, mexican, multi/other\}$.
The factor sexhas two levels: $sex = \{male, female\}$.
The factor educa has five levels: $educa = \{1, 2, 3, 4, 5\}$.
By default, R uses treatment contrasts for categorical variables. In these contrasts, the first value of the factor is used a reference level and the remaining values are tested against the reference. The maximum number of contrasts for a categorical variable equals the number of levels minus one.
The contrasts for race allow testing the following differences:
$race = black\ vs. race = white$, $race = mexican\ vs. race = white$, and $race = multi/other\ vs. race = white$.
For the factor $educa$, the reference level is $1$, the pattern of contrasts is analogous.
These effects can be interpreted as the difference in the dependent variable. In your example, the mean value of cog is $13.8266$ units higher for $educa = 2$ compared to $educa = 1$ (as.factor(educa)2).
One important note: If treatment contrasts for a categorical variable are present in a model, the estimation of further effects is based on the reference level of the categorical variable if interactions between further effects and the categorical variable are included too. If the variable is not part of an interaction, its coefficient corresponds to the average of the the individual slopes of subsets of this varible along all remaining categorical variables. The effects of $race$ and $educa$ correspond to average effects with respect to the factor levels of the other variables. To test overall effects of $race$, you would need to leave $educa$ and $sex$ out of the model.
Numeric variables: $lg\_hag$ and $pdg$
Both lg_hag and pdg are numeric variables hence the coefficients represent the change in the dependent variable associated with an increase of $1$ in the predictor.
In principle, the interpretation of these effects is straightforward. But note that if interations are present, the estimation of the coefficients is based on the references categories of the factors (if treatment contrasts are employed). Since $pdg$ is not part of an interaction, its coefficient corrsespods to the average slope of the variable with respect. The variable $lg\_hag$ is also part of an interaction with $educa$. Therefore, its effect holds for $educa = 1$, the base level.; it is not a test of an overall influence of the numeric variable $lg\_hag$ irrespective of the levels of the factors.
Interactions between categorical and numeric variables: $lg\_hag \times educa$
The model does not only include main effects but also interactions between the numeric variable $lg\_hag$ and the four contrasts associated with $educa$. These effects can be interpreted as the difference in the slopes of $lg\_hag$ between a certain level of $educa$ and the reference level ($educa = 1$).
For example, the coefficient of lg_hag:as.factor(educa)2 (-21.2224) means that slope of $lg\_hag$ is $21.2224$ units lower for $educa = 2$ compared to $educa = 1$.
Best Answer
The predicted value of your dependent variable can be found for any combination of Mown and Decline. When you have an interaction, looking at predicted values (and graphing them) is often a good way to see what is going on. You can also then exponentiate the predicted values.
You have log(RD)=6.984−0.852Decline−4.703Mown+3.030MownDecline
so you could make a table:
You could also make a graph with mown on the x axis, the predicted DV on the y axis, and one line for "decline = 0" and one for "decline = 1"