Use events:
Z0 = 6;
Zt=0.05*6;
tspan = [0 24];
opts = odeset('Events',@(tZ,Z)EventsFcn(tZ,Z,Zt));
[tZ,Z,tZe,Ze,iZe] = ode45(@ConcDCE,tspan,Z0,opts);
plot(tZ,Z)
hold on
scatter(tZe,Ze,'or')
function dZdt=ConcDCE(t,~)
k1=1.26;
k2=0.74;
k3=0.22;
X0=1;
Y0=4;
Z0=6;
dZdt=k2*(Y0*exp(-k2*t)+((X0*k1)/(k2-k1)*(exp(-k1*t)-exp(-k2*t))))-k3*(Z0*exp(-k3*t)+((Y0*k2)/(k3-k2)*(exp(-k2*t)-exp(-k3*t)))+X0*k1*k2*((exp(-k1*t))/((k2-k1)*(k3-k1))-(exp(-k2*t))/((k2-k1)*(k3-k2))+(exp(-k3*t))/((k3-k1)*(k3-k2))));
end
function [Conc,isterminal,direction] = EventsFcn(~,Z,Zt)
Conc = Z - Zt; % The value that we want to be zero
isterminal = 0; % Halt integration
direction = 0; % The zero can be approached from either direction
end
