It depends on how your moderator variable is scaled. Does a high value indicates a high support or a low support?

Thank you so much Josefine Atzendorf, In my research, high value (5) indicates high support and low value (1) indicates low support.......In this sense, what will be the possible explanations?

The negative sign on your moderator variable may be due to confounding. Without loss of generality, say your indicator for support is strongly related to (a) whether the individual is a civil servant or not and (b) to her socio-economic (SE) status . Suppose the effect of channel (a) on job satisfation is completely mediated by her being more successful at managing her work-family time allocation and therefore having lower work-family conflict vis-a-vis someone who is not a civil servant (I am thinking of allowances, more flexible working hours, etc..). What is left as a direct effect of support on job satisfaction is via channel (b) i.e. the fraction of it received for being from a relatively disadvantaged SE background. So (the omission of) SE status is the confounder here in that the negative effect of support on job satisfaction that you find in the data may actually be channelling the negative effect of SE status on your dependent variable, if any. I'd try to also include a proxy for SE status in the model and see what happens.

Thank you so much Luca Mancini

When the direct relationship between the IV (G) and DV (F) is not supported but the relationship is moderated by (B) supported with a negative beta (-0.144) How do you interpret that when the slope for High (B) is steeper than Low (B)?