LFS booting EFI in macbook pro 2014

I am trying to build linux from scratch (LFS) as an educational project using the main LFS book version 12.1 , however, whene i reach the bottable chapter, i found that i have to boot my LFS using EFI support because my main machine is macbook pro 2014, so i follwo the BLFS guide Using GRUB to Set Up the Boot Process with UEFI , and https://www.linuxfromscratch.org/blfs/view/12.1/postlfs/grub-efi.html ; whene i re-boot the machine i get > error disk 'hd0,2' not found I fix it by using > set root=(hd1,gpt4) The next problem is > /boot/vmlinuz-6.7.4-lfs-12.1 not found i checked my boot file and found the file name exists under differnt name **/boot/vmlinuz-6.7.4-lfs-12.1-systemd** so i rename it to **/boot/vmlinuz-6.7.4-lfs-12.1**. No whene i am booting again i get a black screen after selecting the lfs system from booting menu . attached files > **fdisk -l /dev/sda outputs** Device Start End Sectors Size Type /dev/sda1 40 409639 409600 200M EFI System /dev/sda2 411648 17807359 17395712 8.3G Linux swap /dev/sda3 488847608 490117143 1269536 619.9M Apple boot /dev/sda4 19855360 81295359 61440000 29.3G Linux filesystem linux kernel configuration file grub.cfg file any help!