Hayes' PROCESS Macro (which will test your model) works within SPSS: You don't need to install or open or use AMOS. 

There's an introduction to the PROCESS Macro (inc. references) in here as well as references and citations for alternative approaches using SEM:

https://www.researchgate.net/publication/303818191_Interaction_Moderation_and_Mediation_Definitions_Discrimination_and_some_means_of_testing

Presentation Interaction, Moderation, and Mediation: Definitions, Discrim...

Thanks James .. i haven't actually look at PROCESS yet but will do so after familiarizing myself with its concept. My concern is spss runs based on composite variables but mine are latent variables.

No problem.  :-) 

For mediation through latent variables, PROCESS won't help you unless you create these variables through PCA or EFA approaches before hand.  ...But then you might as well use an SEM programme like AMOS at that point.  AMOS will calculate indirect effects for you (via the bootstrapping method) to estimate the x-m1-m2-y pathway (it's in the text output file).  If these four measures are not all continuous though, I suggest referring to Hayes' journal papers for tips on how to caculate the total indirect, and total effects of X on Y. e.g. http://onlinelibrary.wiley.com/doi/10.1111/bmsp.12028/abstract

In terms of good textbooks for AMOS and SEM, I swear by, "Tabachnick, B.G. Fidell, L.S. (2013).  Using Multivariate Statistics.  Sixth Edition. Boston: Pearson."

I hope that this helps.

Hi James. Thanks for your suggestions. Yeap I bootstrapped using AMOS. I also used Hair et al (2014)'s variance accounted for (VAF) formula to determine the mediation effect.