Hi,
will SDHC card (4 GB) work with the SPI interface of the LPC214x development board ?
SPI+SD/SDHC/SDXC is pretty platform agnostic. Yes, an SDHC card can be used via an SPI interface, got some 32GB ones working here. You'll need to pick/code a driver that supports the command set of the SDHC, above the normal SD/MMC ones.