Can we use `two way anova` when factors have interaction? 
You should have independence of observations, which means that there
  is no relationship between the observations in each group or between
  the groups themselves.

Above sentence come from https://statistics.laerd.com/spss-tutorials/two-way-anova-using-spss-statistics.php when introduce two way anova requirements.  
Then I think factors interaction is not allowed in two way anova,otherwise violet the data requirement.
But I found a two way anova example in http://www.sthda.com/english/wiki/two-way-anova-test-in-r as below:  
# Two-way ANOVA with interaction effect
# These two calls are equivalent
res.aov3 <- aov(len ~ supp * dose, data = my_data)

I am confused,can we use two way anova when factors have interaction?
 A: Suppose you have three levels of Factor A and two levels of Factor B.
That makes $3(2) = 6$ 'cells' in your data table. If you have $r \ge 2$ independent measurements within each cell (called 'replications'), then you would have an interaction term (below denoted $\gamma_{ij})$ in your ANOVA model.
$$Y{ijk} = \mu + \alpha_i + \beta_j + \gamma_{ij} + e_{ijk},$$
where $i = 1,2,3;\; j=1,2; \, k = 1, 2, \dots, r$ and $e_{ijk} \stackrel{iid}{\sim}\mathsf{Norm}(0, \sigma).$
Your ANOVA table will have rows with degrees of freedom (DF) as shown below (different texts and programs have various column labels and the TOTAL line may be
omitted):
Factor   DF    SS    MS    F
     A    2
     B    1
   A*B    2
 Resid  6(r-1)
 TOTAL   6r-1

If the number of replications per cell is $r = 1,$ then you cannot
have an interaction term in your ANOVA model. In that case, interaction may truly be
present, but you would not be able to test for its presence.
Example: Suppose observations are crop yields in $6r$ plots with independent
planting of crops. Let Factor A be three levels of fertilizer and Factor B be two levels of irrigation. If there is no interaction,
more fertilizer and heavier irrigation might be additive effects.
An interaction might occur if the highest level of fertilization requires the highest level of irrigation, otherwise the plants
are 'burned' by the extra fertilizer. Then the corresponding
$\gamma_{31}$ term in the model might be negative. If interaction is significant, then you have to be careful interpreting a significant
main effect. For example, maybe you couldn't say, without qualification, 
 "increasing fertilizer increases yield."
